A Hike through the Swampland
2022-03-17 09:30 - 11:00 (America/New_York)
Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.

Non-zero momentum requires long-range entanglement
2022-03-23 10:30 - 12:00
Youtube Video

Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.

Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor
2022-03-24 09:30 - 11:00
Youtube Video

Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).

Renormalization group flow as optimal transport
2022-03-30 10:30 - 12:00
Youtube Video

Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem. The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories. Our techniques generalize to other RG flow equations beyond Polchinski’s.

Late time von Neumann entropy and measurement-induced phase transition
2022-04-06 10:30 - 12:00 | Virtual
Youtube Video

Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

Lattice Gauge Theory View of Toric Codes, X-cube, and More
2022-04-07 09:30 - 11:00 | Virtual
Youtube Video

Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References:
[1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021)
[1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022)
[2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation.
[3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.

Why is the mission impossible? Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
2022-04-13 20:30 - 22:00 | Virtual
Youtube Video
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.

Cancellation of the vacuum energy and Weyl anomaly in the standard model, and a two-sheeted, CPT-symmetric universe
2022-04-14 09:30 - 11:00 | Virtual
Youtube video

Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).
As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.
(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

Higgs = SPT
2022-04-22 15:30 - 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Ruben Verresen
Title: Higgs = SPT
Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.

Aspects of 4d supersymmetric dynamics and geometry
2022-04-28 10:30 - 12:00 | Virtual
Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.

Cosmology from the vacuum
2022-05-11 10:30 - 12:00
Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.

Oblique Lessons from the W Mass Measurement at CDF II
2022-05-12 10:30 - 12:00
Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

The Generalized Landau Paradigm (a review of generalized symmetries in condensed matter)
2022-05-18 16:00 - 17:30 | Virtual
Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045

Boundary conditions and LSM anomalies of conformal field theories in 1+1 dimensions
2022-05-18 16:00 - 17:30 | Virtual
Speaker: Linhao Li (ISSP, U Tokyo)
Title: Boundary conditions and LSM anomalies of conformal field theories in 1+1 dimensions
Abstract: In this talk, we will study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state which is invariant under a symmetry, then the CFT can be gapped with a unique ground state by adding the corresponding gapping potential. This means that the symmetry of the CFT is anomaly free. Using this approach, we will systematically deduce the anomaly-free conditions for various types of CFTs with several different symmetries. When the symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis type ingappability of the system. Our results are consistent with, where available, known results in the literature. Moreover, we extend the discussion to other symmetries including spin groups and generalized time-reversal symmetries. As an application, we propose 1d LSM theorem involving magnetic space group symmetries on the lattice. The extended LSM theorems apply to systems with a broader class of spin interactions, such as Dzyaloshinskii-Moriya interactions and chiral three-spin interactions.

Oblique Lessons from the W Mass Measurement at CDF II
2022-05-25 10:30 - 12:00 | Hybrid
Speaker: Seth Koren (University of Chicago)
Title: Baryon Minus Lepton Number BF Theory for the Cosmological Lithium Problem
Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+ → 3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.

Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: Recent developments
2022-07-07 10:30 - 12:30 | Virtual
Speaker: Kenichi Konishi (UNIPI.IT)
Title: Anomalies, dynamics and phases in strongly-coupled chiral gauge theories: Recent developments
Abstract: After many years of efforts, still very little is known today about the physics of strongly-coupled chiral gauge theories in four dimensions, in spite of an important role they might play in the physics of fundamental interactions beyond the standard SU(3)xSU(2)xU(1) model. This is in stark contrast with the vectorlike gauge theories for which we have many solid results, thanks to some exact theorems, to the lattice simulation studies, to the Seiberg-Witten exact solution of N=2 supersymmetric gauge theories, and last, but not the least, to the real-world strong-interaction phenomenology and experimental tests of Quantum Chromodynamics.
The purpose of this seminar is to discuss the results of our recent efforts to improve the understanding of the strongly-coupled chiral gauge theories. Among the main tools of analysis are the consideration of anomalies. We use both the conventional ’t Hooft anomaly-matching ideas, and new, more stringent constraints coming from the generalized anomalies involving some higher-form symmetries. Also, the so-called strong anomalies, little considered in the context of chiral gage theories, are found to carry significant implications.
As the playground we study several classes of SU(N) gauge theories, the so-called Bars-Yankielowicz models, the generalized Georgi-Glashow models, as well as a few other simple theories with the fermions in complex, anomaly-free representations of the color SU(N).
Color-flavor-locked dynamical Higgs phase and dynamical Abelianization, emerge, among others, as two particularly interesting possible phases the system can flow into in the infrared, depending on the matter fermion content of the model.

Transport in large-N critical Fermi surface
2022-08-16 10:00 - 11:30 | Virtual
Speaker: Haoyu Guo (Harvard)
Title: Transport in large-N critical Fermi surface

Abstract: A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermion-scalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and show that a previously proposed omega^{-2/3} contribution to the optical conductivity at frequency omega has vanishing co-efficient. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity behaves like a Fermi liquid. Arxiv references: 2203.04990, 2207.08841

Gifts from anomalies: new results on quantum critical transport in non- Fermi liquids
2022-09-07 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Zhengyan Darius Shi (MIT)

Title: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
Abstract: Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result due to Kim et al. is incorrect for inversion-odd order parameters.

Non-invertible Symmetries in Nature
2022-09-13 09:30 - 11:00
Quantum Matter in Mathematics and Physics

Speaker: Yichul Cho (SUNY Stony Brook)
Title: Non-invertible Symmetries in Nature
Abstract: In this talk, I will discuss non-invertible symmetries in
familiar 3+1d quantum field theories describing our Nature. In
massless QED, the classical U(1) axial symmetry is not completely
broken by the ABJ anomaly. Instead, it turns into a discrete,
non-invertible symmetry. The non-invertible symmetry operator is
obtained by dressing the naïve U(1) axial symmetry operator with a
fractional quantum Hall state. We also find a similar non-invertible
symmetry in the massless limit of QCD, which provides an alternative
explanation for the neutral pion decay. In the latter part of the
talk, I will discuss non-invertible time-reversal symmetries in 3+1d
gauge theories. In particular, I will show that in free Maxwell
theory, there exists a non-invertible time-reversal symmetry at every
rational value of the theta angle.
Based on https://arxiv.org/abs/2205.05086 and https://arxiv.org/abs/2208.04331.

Candidates for Non-Supersymmetric Dualities
2022-09-26 09:00 - 10:30 | Virtual
Quantum Matter in Mathematics and Physics
Speaker: Avner Karasik (University of Cambridge, UK)
Title: Candidates for Non-Supersymmetric Dualities
Abstract: In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

Holomorphic Twists and Confinement in N=1 SYM
2022-10-04 09:30 - 11:00 | Virtual
Quantum Matter Seminar
Speaker: Justin Kulp (Perimeter Institute)
Title: Holomorphic Twists and Confinement in N=1 SYM
Abstract: Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

Topological Wick Rotation and Holographic duality
2022-10-17 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Liang Kong (Sustech)
Title: Topological Wick Rotation and Holographic duality
Abstract: I will explain a new type of holographic dualities between
n+1D topological orders with a chosen boundary condition and nD
(potentially gapless) quantum liquids. It is based on the idea of
topological Wick rotation, a notion which was first used in
arXiv:1705.01087 and was named, emphasized and generalized later in
arXiv:1905.04924. Examples of these holographic dualities include the
duality between 2+1D toric code model and 1+1D Ising chain and its
finite-group generalizations (independently discovered by many
others); those between 2+1D topological orders and 1+1D rational
conformal field theories; and those between n+1D finite gauge theories
with a gapped boundary and nD gapped quantum liquids. I will also
briefly discuss some generalizations of this holographic duality and
its relation to AdS/CFT duality.

On the six-dimensional origin of non-invertible symmetries
2022-10-18 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Michele Del Zotto (Uppsala University)
Title: On the six-dimensional origin of non-invertible symmetries
Abstract: I will present a review about recent progress in charting non-invertible symmetries for four-dimensional quantum field theories that have a six-dimensional origin. These include in particular N=4 supersymmetric Yang-Mills theories, and also a large class of N=2 supersymmetric theories which are conformal and do not have a conventional Lagrangian description (the so-called theories of “class S”). Among the main results, I will explain criteria for identifying examples of systems with intrinsic and non-intrinsic non-invertible symmetries, as well as explore their higher dimensional origin. This seminar is based on joint works with Vladimir Bashmakov, Azeem Hasan, and Justin Kaidi.

Insulating BECs and other surprises in dipole-conserving systems
2022-10-24 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Ethan Lake (MIT)
Title: Insulating BECs and other surprises in dipole-conserving systems
Abstract: I will discuss recent work on bosonic models whose dynamics conserves both total charge and total dipole moment, a situation which can be engineered in strongly tilted optical lattices. Related models have received significant attention recently for their interesting out-of-equilibrium dynamics, but analytic and numeric studies reveal that they also possess rather unusual ground states. I will focus in particular on a dipole-conserving variant of the Bose-Hubbard model, which realizes an unusual phase of matter that possesses a Bose-Einstein condensate, but which is nevertheless insulating, and has zero superfluid weight. Time permitting, I will also describe the physics of a regime in which these models spontaneously fracture into an exotic type of glassy state.

Unorientable Quantum Field Theories: From crosscaps to holography
2022-10-25 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: João Caetano (CERN)
Title: Unorientable Quantum Field Theories: From crosscaps to holography
Abstract: In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state.

In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4-manifold. I will show how to do this in the example of N=4 Supersymmetric Yang-Mills, discuss its holographic description and present a new solvable setup of AdS/CFT.

Kardar-Parisi-Zhang dynamics in integrable quantum magnets
2022-11-01 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Francisco Machado (Berkeley/Harvard)
Title: Kardar-Parisi-Zhang dynamics in integrable quantum magnets
Abstract: Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.
In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.
Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.
[1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
(PRL in press) – arXiv:2205.02853
[2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
Science (2022) — arXiv:2107.00038

Topological symmetry in field theory
2022-11-08 11:30 - 13:00 | Virtual
Quantum Matter Seminar
Speaker: Daniel S. Freed (U Texas)
Title: Topological symmetry in field theory
Abstract: Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries,” “higher symmetries,” “noninvertible symmetries,” etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory. This is joint work with Constantin Teleman and Greg Moore.

Topology of the Fermi sea: Ordinary metals as topological materials
2022-11-15 09:30 - 11:00
Quantum Matter Seminar
Speaker: Pok Man Tam (University of Pennsylvania)
Title: Topology of the Fermi sea: Ordinary metals as topological materials
Abstract: It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F to experimental observables, namely: (i) equal-time density/number correlations [1], and (ii) Andreev state transport along a planar Josephson junction [2]. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.
[1] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)
[2] P. M. Tam and C. L. Kane, arXiv:2210.08048

3D gravity and gravitational entanglement entropy
2022-11-22 09:30 - 11:00 | Virtual
Quantum Matter Seminar
Speaker: Gabriel Wong (Harvard CMSA)
Title: 3D gravity and gravitational entanglement entropy
Abstract: Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime. Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge modes.

Symmetry in quantum field theory and quantum gravity 1
2022-12-01 10:30 - 11:30
Speaker: Daniel Harlow (MIT)
Title: Symmetry in quantum field theory and quantum gravity 1
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).
