Quantum Matter/Condensed Matter Seminars

Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. Links to connect can be found in the schedule below once they are created. 

As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place Wednesdays from 10:30 – 12:00pm on Zoom.  The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm on Zoom.  Please email the seminar organizer to obtain a link. The schedules for both seminars will be updated below as speakers are confirmed:

Spring 2020:

Date Speaker Title/Abstract
2/5/2020 Ya-Hui Zhang (Harvard)



Title: A new theory for pseudogap metal in hole doped cuprates

Abstract: We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework. For the pseudogap metal, “Fermi arc” observed in ARPES can be naturally reproduced. We also provide a theory for a critical point across which the carrier density jumps from x to 1+x. We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and generic SU(N) Hubbard model.

2/6/2020 Yuan Cao (MIT) Title: Twistronics in Graphene Superlattices: Correlation and Superconductivity
2/12/2020 Xue-Yang Song (Harvard)


Title: Monopoles in QED3 Dirac Spin Liquids
2/13/2020 Grigory Tarnopolskiy (Harvard)


Title: Spontaneous symmetry breaking in SYK models
2/19/2020 Zhehao Dai (MIT)


Title: Modeling the pseudogap state in cuprates: quantum disordered pair density wave

Abstract: I will briefly review the pseudogap phenomenology in high Tc cuprate superconductors, especially recent experiments related to charge density waves and pair density waves, and propose a simple theory of the pseudogap. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and a nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

2/20/2020 Lokman Tsui (MIT)


Title: Lattice models that realize $Z_n$ 1-symmetry-protected topological states for even $n$

Abstract: Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low energies. The low energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry protected topological order. This motivates us, as a simplest example, to study a lattice model of $Z_n$-1-symmetry protected topological (1-SPT) states in 3+1D for even $n$. We write down an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with non-trivial self-statistics. For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double semion topological order for $m=1$ and toric code for $m=2$. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry.



Wei Zhang (MIT)


Title: “Cohomology of Shimura Variety”
2/27/2020 Nat Tantivasadakarn (Harvard)


Title: Jordan-Wigner Dualities for translation-invariant Hamiltonians in any dimension

Abstract: Inspired by recent constructions of Jordan-Wigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translation-invariant model of spinless fermions to gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly many-body) “hopping” operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translation-invariant Hamiltonians proposed by Haah. 

I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be “fermionic”. This may give rise to new non-relativistic ‘t Hooft anomalies.



Robert Gompf (UT Austin)


Title: Cutting and pasting 4-manifolds

Abstract: We will discuss techniques topologists use for understanding 4-manifolds obtained by cut-and-paste constructions. The hope is that these techniques may be useful for understanding 4-dimensional topological field theories.

3/5/2020 Cancelled   
3/11/2020 Zhengwei Liu (Harvard) 


Title: Quantized Graphs and Quantum Error Correction

Abstract: Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a general framework. We give a new method to construct graphical quantum error correcting codes on quantized graphs and characterize all optimal ones. We establish a further connection to geometric group theory and construct quantum low-density parity-check stabilizer codes on the Cayley graphs of groups. Their logical qubits can be encoded by the ground states of newly constructed exactly solvable models with translation-invariant local Hamiltonians. Moreover, the Hamiltonian is gapped in the large limit when the underlying group is infinite.

3/12/2020  Cancelled  
3/18/2020 Spring Break  
3/19/2020 Spring Break   
3/25/2020 Zhehao Dai (MIT) 

Title: Fluctuating pair density wave in cuprates

Abstract: Recent high-field low-temperature data shed new light on the mysterious pseudogap phase in cuprates. I will introduce a simple way to synthesize the low-temperature data, the charge density wave, and the previous ARPES and optical data. In the meantime, I will discuss the general problem of how fluctuating superconducting order changes the fermion spectrum and other response functions.

3/26/2020  Cancelled
4/1/2020 Jong Yeon Lee (Harvard)   This meeting will be taking place virtually on Zoom.Title: Exploration on Deconfined Fractionalized Particles at Quantum Criticality — Fractional Chern Insulators and Shastry-Sutherland Quantum Magnets

Abstract: One of the most exotic phenomena in condensed matter systems is the emergence of fractionalized particles. However, until now, only a few experimental systems are known to realize fractionalized excitations. This calls for more systematic ways to find and understand systems with fractionalization. One natural starting point is to look for an exotic quantum criticality, where the fundamental degrees of freedom become insufficient to describe the system accurately. Furthermore, understandings in exotic quantum critical phenomena would provide a unified perspective on nearby gapped phases, i.e. a guiding principle to engineer the system in a desirable direction that may host anyons. In this talk, I would present my works on two different types of quantum criticality: (1) Deconfined quantum critical point (DQCP) between plaquette valence-bond solids and Neel ordered state in Shastry-Sutherland lattice models [PRX 9, 041037 (2019)], where two distinct symmetry breaking order parameters become unified by the fractionalized degree of freedom. (2) Transitions between fractional Chern/Quantum Hall insulators tuned by the strength of lattice potential [PRX 8, 031015 (2018)]. Here, the low-lying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by Chern-Simons quantum electrodynamics. The numerical results using iDMRG as well as theoretical analysis of their emergent critical properties would be presented. In the end, I would discuss their spectroscopic signatures, providing a full analysis of experimental verification.

4/2/2020   This meeting will be taking place virtually on Zoom.
4/8/2020 Chang-Tse Hsieh (IPMU and U Tokyo)   This meeting will be taking place virtually on Zoom.Title: Anomaly of the Electromagnetic Duality of Maxwell Theory

Abstract: Every physicist knows that the classical electromagnetism is described by Maxwell’s equations and that it is invariant under the electromagnetic duality S: (E, B) → (B, −E). However, the properties of the electromagnetic duality in the quantum theory might not be as well known to physicists in general, and in fact are not very well understood in the literature. This is particularly true when going around a nontrivial path in the spacetime results in a duality transformation. In our recent work, we uncovered a feature of the Maxwell theory and its duality symmetry in such a situation, namely that it has a quantum anomaly. We found that the anomaly of this system in a particular formulation is 56 times that of a Weyl fermion. Our result reproduces, as a special case, the known anomaly of the all-fermion electrodynamics—a version of the Maxwell theory where particles of odd (electric or magnetic) charge are fermions—discovered in the last few years.

4/9/2020   This meeting will be taking place virtually on Zoom.
4/15/2020   This meeting will be taking place virtually on Zoom.
4/16/2020   This meeting will be taking place virtually on Zoom.
4/22/2020   This meeting will be taking place virtually on Zoom.
4/23/2020   This meeting will be taking place virtually on Zoom.
4/29/2020   This meeting will be taking place virtually on Zoom.
4/30/2020   This meeting will be taking place virtually on Zoom.





Fall 2019:

Date Speaker Title/Abstract
9/05/2019 Juven Wang (Harvard CMSA) Title: Quantum Matter Basics for Mathematicians
9/18/2019 Po-shen Hsin (Caltech)


Title: Lorentz symmetry fractionalization and duality in (2+1)d

Abstract: I will introduce a discrete transformation in bosonic QFTs with Z2 one-form symmetry using the concept of symmetry fractionalization in condensed matter physics. I will then discuss some applications including boson/fermion dualities in (2+1)d.

9/19/2019 Poshen Hsin (Caltech) Title: “3d duality”

Members’ Seminar

Ryohei Kobayashi (U of Tokyo) Title: Fermionic phases of matter on unoriented spacetime
9/25/2019 Juven Wang (CMSA)


Title: Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon

Abstract: We introduce a new class of tensor field theories in any dimension that has an interesting mixing between symmetric-tensor gauge theory and anti-symmetric tensor topological field theory. The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory may be a new gem sitting in the virgin territory outside the familiar gauge theories — outside the paradigm of Maxwell theory in 1865 and Yang-Mills theory in 1954. We discuss its relation to the non-abelian generalization of Fracton in condensed matter, and Embeddon that we will introduce. This is based on https://arxiv.org/abs/1909.13879, jointly with Kai Xu (Harvard).

9/26/2019 Shu-Heng Shao (IAS)


Title: Anomalies and Charged Operators

Abstract: We study the implications of ‘t Hooft anomaly for conformal field theory. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z2 global symmetry are derived. We find that there is a universal upper bound on the lightest Z2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous.

We further discuss the implications for the Weak Gravity Conjecture in AdS3/CFT2.  Finally we present a conjecture on more general anomalies that cannot be matched by TQFTs, a notion known as the “symmetry-protected gaplessness” in condensed matter physics.



Zhen Bi (MIT) 


Title: Novel quantum criticality beyond Landau-Ginzburg-Wilson-Fisher paradigm

Abstract: The infrared behavior of 3 + 1-D non-abelian gauge fields with massless matter fields is an extremely important and intensively studied topic in particle physics. In this talk, we asking the following question from a condensed matter perspective: given some deconfined gauge theory in 3 + 1-D, what phase transition can this theory describe? It turns out to be a fruitful way to think about these gauge theories and provides many explicit examples for several novel quantum critical phenomena. 1. We present several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D for both bosonic and fermionic systems. 2. We find situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. 3. We exhibit the possibility – which we dub “unnecessary quantum critical points” – of stable generic continuous phase transitions within the same phase. 4. We present examples of interaction driven band-theory forbidden continuous phase transitions between two distinct band insulators. 5. We find an example for a Landau-allowed quantum phase transition, however, with a critical theory that is beyond Landau description.

10/3/2019 Ryan Thorngren (CMSA)


Title: Domain Walls and the CPT Theorem

Abstract: I will describe how in a relativistic quantum field theory, symmetry-broken domain walls enjoy a curious remnant of the broken symmetry obtained by a combination with the unbreakable CPT symmetry. There is an anomaly-matching condition relating the symmetry-preserving bulk phase to the anomaly on the wall. This condition is related to an interesting property of manifold cobordisms called the Smith isomorphism. I will prove some generalizations of the Smith isomorphism theorem and discuss some physics applications to superfluids and gauge theories. This is joint work with Itamar Hason and Zohar Komargodski.

10/4/2019 Liang Kong (Shenzhen Institute of Quantum Sciences and Engineering, Southern University of Science and Technology) 


Title: A unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders

Abstract: It was well known that a gapless boundary of a 2+1D topological order is different from and significantly richer than a gapped boundary. In this talk, however, we will propose a unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders. In particular, we will show that observables on the 1+1D world sheet of a chiral gapless boundary in the long wave length limit form an enriched fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. If time permits, we will also briefly discuss some consequences of this result, including a theory of non-chiral gapless boundaries, applications to boundary topological phase transitions, 0+1D defects between different gapless boundaries and a generalized boundary-bulk relation. This is joint work with Hao Zheng.

10/9/2019 Peter Koroteev (Berkeley) 


Title: On Quiver W-algebras and Defects from Gauge Origami

Abstract: Using Nekrasov’s gauge origami framework, we study two different versions of the BPS/CFT correspondence – first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by Kimura and Pestun. The gauge origami enables us to work with both dualities simultaneously and find exact matchings between the parameters. In our main example of an A-type quiver gauge theory, we show that the corresponding quiver qW-algebra and its representations are closely related to a large-n limit of spherical gl(n) double affine Hecke algebra whose modules are described by instanton partition functions of a defect quiver theory.

10/10/2019 Julio Parra Martinez (UCLA)


Title: GSO projections and D-brane classification via SPT phases

Abstract: I will explain how a choice of fermionic SPT phases on the string worldsheet gives rise to the different GSO projections. This point of view not only easily explains why there are essentially two type II and 0 theories, but also predicts an eight-fold classification of unoriented Pin- type 0 theories. A similar analysis for unoriented Type II strings requires introducing Double Pin (DPin) structures, and confirms that there is an essentially unique choice of the type I worldsheet theory. By considering the implications of the bulk SPTs on the boundary of opens strings we provide an alternative route to the K-theoretic classification of D-branes, and clarify some of their properties. As an example, I will describe the classification of D-branes in the unoriented Pin- type 0 theories, in which all higher real K-groups play a role.



Kantaro Ohmori (SUNY SCGP) Title: Anomaly Obstructions to Symmetry Preserving Gapped Phases: Discrete symmetry case


Abstract: Anomalies are renormalization group invariants and constrain the dynamics of quantum field theories. In this talk we show that certain anomalies for discrete global generalized symmetries imply that the underlying theory either spontaneously breaks its global symmetry or is gapless. This is done by observing that a symmetry preserving unitary TQFT is not compatible with the anomaly whose inflow action evaluates nontrivially on a certain manifold.

10/17/2019 No Seminar  
10/23/2019  Chong Wang (Perimeter)


Title: Unquantized quantum anomalies: electric polarization, Luttinger theorem and correlated Weyl semimetals
10/24/2019 Andrew Turner (MIT) 


Title: General F-theory models with SU(3) x SU(2) x U(1) / Z_6 symmetry

Abstract: We construct a general form for an F-theory Weierstrass model over any base giving a 6D or 4D supergravity theory with gauge group SU(3) x SU(2) x U(1) / Z_6 and associated generic matter. The concept of ‘generic matter’ can be rigorously defined in 6D supergravity and generalizes naturally to four dimensions for F-theory models. We describe general F-theory models with this gauge group and the associated generic matter content, which fit into two distinct classes, and present an explicit Weierstrass model that realizes these models as two distinct branches. We also discuss, as a special case, the class of models recently studied by Cvetic, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing.



Chong Wang (Perimeter)  Title: A theory of deconfined pseudo-criticality
10/31/2019 Patrick Lee (MIT)


Title: Gapless spin liquid and emergent gauge theory

Abstract: I shall review the emergence of gauge theory as a description of quantum spin liquid, particularly the gapless variety. The matter field plays a key role in stabilizing the deconfined phase. I shall also discuss the current experimental status of gapless spin liquid candidates, including the recently “re-discovered” example of TaS2.

11/6/2019 Dan Freed (UT Austin)


Title: M-theory is time-reversal invariant

Abstract: In joint work with Mike Hopkins we prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. There are two sources of anomalies: the Rarita-Schwinger field and the cubic form for the C-field. I will explain the general principles behind these anomalies, since they apply in many problems. Then I’ll turn to the specific computations we did to verify this anomaly cancellation. They include topologial and geometric methods for computing eta-invariants as well as homotopy-theoretic techniques for computing bordism groups.

11/7/2019 Mathias Scheurer (Harvard) Title: Gauge theories for the cuprates:thermal Hall effect and optimal doping

Abstract: Recent experiments [1] have revealed an enhanced thermal Hall effect in the pseudogap phase of several different cuprate compounds. The large signal even persists in the undoped system and, thus, challenges our understanding of the square-lattice antiferromagnet fundamentally. In the first part of the talk, I will analyze possible mechanisms that can give rise to a thermal Hall effect in the antiferromagnet [2,3]. In particular, I will discuss the possibility [3] that the magnetic field can drive the Néel state close to a transition to a phase where Néel order coexists with a chiral spin liquid. A spinon lattice model for this transition is shown to give rise to a large thermal Hall conductivity that also features a magnetic-field and temperature dependence similar to experiment. We will derive the low-energy continuum field theory for the transition, which is characterized by an emergent global SO(3) symmetry and has four different formulations that are all related by dualities. If time permits, I will present, in the second part of the talk, a non-Abelian gauge theory that we propose [4] as an effective field theory for the cuprates near optimal doping. In this theory, spin-density-wave order is fractionalized into Higgs fields while all low-energy fermionic excitations are electron-like and gauge neutral. The conventional Fermi-liquid state corresponds to the confining phase of the theory at large doping and there is a quantum phase transition to a Higgs phase, describing the pseudogap, at low doping. It will be shown that the topological order of the Higgs phase is very naturally intertwined with charge-density-wave, Ising-nematic, and scalar spin-chirality order. We will also discuss the quantum critical point of the model.



Michael Pretko (U Colorado) Title:  Introduction to Fractons

Abstract:  A fracton is an exotic new type of emergent quasiparticle with restricted mobility.  While a single fracton is strictly immobile in isolation, they can often come together to form certain mobile bound states.  In this talk, I will give a bird’s-eye overview on the current state of the field of fractons. I will begin with the theoretical formalism for fractons in terms of symmetric tensor gauge theories, which possess unusual higher moment conservation laws.  I will then outline some physical realizations of fractons, such as spin models and topological crystalline defects, the latter of which arises through a novel field theory duality. Finally, I will discuss some of the most interesting phenomenology of fracton systems, such as their non-ergodic and gravitational behavior.



Michael Pretko (U Colorado) Title:  Advances in Fracton Physics: Dualities, Field Theories, and Classification

Abstract:  In this talk, I will give short informal explanations of three topics in the field of fractons with some interesting mathematical structure.  I will begin with a detailed discussion of fracton-elasticity duality, relating the properties of tensor gauge theories to the elastic description of two-dimensional crystals.  I will emphasize the role of symmetries in this duality, and also discuss how the duality extends to three dimensions, giving rise to “higher-form” analogues of fracton conservation laws.  Next, I will discuss recent advances on the field theory description of fractons, showing how fractons can be obtained by gauging field theories with a “vector” global symmetry. Finally, I will describe recent work towards classifying fracton phases in terms of their fusion theory, which can be described as a module over the group ring of translations.

11/20/2019 Subir Sachdev (Harvard)


Title: Models of optimal doping criticality in the cuprate superconductors

Abstract: There is now much experimental evidence for a significant change in the electronic structure of cuprate superconductors near a hole doping p=p_c optimal for superconductivity. Only for p > p_c do the electronic properties agree with the predictions of band theory. We argue that the data supports the existence of a quantum critical point (QCP) at p=p_c, and for p < p_c we have a novel state characterized by emergent gauge fields, possibly co-existing with conventional symmetry breaking orders. We present evidence that such a QCP is present in the Hubbard model with random, and all-to-all, hopping and exchange. We also discuss a SU(2) gauge theory for the QCP in model of fluctuating incommensurate spin density waves in the absence of disorder.

11/21/2019 Natalie Paquette (Caltech)


Title: Koszul duality in field theory & holography
11/25/2019 Yu-An Chen (Caltech)


Title:  Exact bosonization in higher dimensions and the duality between supercohomology fermionic SPT and higher-group bosonic SPT phases

Abstract: The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any simply connected manifold in 2d, 3d and general dimensions. This gives a duality between all fermionic systems and a new class of lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is exactly equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action. We can increase the code distance of this mapping, such that this mapping can correct all 1-qubit and 2-qubits errors and is useful for the simulation of fermions on the quantum computer. The second part of my talk is about SPT phases. By the boson-fermion duality, we are able to show the equivalent between any supercohomology fermionic SPT and some higher-group bosonic SPT phases. Particularly in (3+1)D, we have constructed a unitary quantum circuit for any supercohomology fermionic SPT state with gapped boundary construction. This fermionic SPT state is derived by gauging higher-form symmetry in the higher-group bosonic SPT and ungauging the fermion parity. The bulk-boundary correspondence in (3+1)D fermion SPT phases will also be briefly discussed.

11/27/2019 Meng Cheng (Yale) 


Title: Gapped boundary of symmetric topological phases and relative anomalies in (1+1)d CFTs

Abstract: Many (2+1)d topological phases admit gapped boundaries. In the presence of global symmetry, the classification of symmetric boundary conditions is further enriched. I will discuss recent work on classifying such boundary conditions for a doubled topological phase, and a general construction of such boundaries in symmetry-enriched string-net models using module categories. I will also describe how the results can be used to compute relative ’t Hooft anomalies in (1+1)d CFTs algebraically.

12/3/2019 Quantum Matter workshop  
12/5/2019 Yizhi You (Princeton)


Title: Emergent fractons and algebraic quantum liquid from plaquette melting transitions

Abstract: Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this talk, I will show that the defects of the valence plaquette solid(VPS) order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints in the VPS phase. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist near QCP, can potentially inhibit the condensation of spinons and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by the proliferation

of spinon dipoles. In particular, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long-range entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization.




Nick G. Jones (University of Bristol) Title: Toeplitz determinants and correlations in topological quantum chains

Abstract: Topological phases protected by symmetry can occur in both gapped and critical systems. I will discuss recent work on such phases for non-interacting fermions in one dimension with spinless time-reversal symmetry. I will show how the phases are classified by a topological invariant and a central charge, explaining also the connection to edge modes. The bulk order parameters of these phases are correlators of fermionic string operators. I will explain how to derive exact asymptotics of these correlation functions using Toeplitz determinant theory, giving insight into the interplay between topology and criticality.

This is largely based on the papers:

Asymptotic correlations in gapped and critical topological phases of 1D quantum systems, N. G. Jones and R. Verresen, J. Stat. Phys. 175 (2019)

Topology and edge modes in quantum critical chains, R. Verresen, N. G. Jones and F. Pollmann, Phys. Rev. Lett. 120 (2018)

12/11/2019 Yuya Tanizaki (NCSU)


Title: Constraints on possible dynamics of QCD by symmetry and anomaly


Abstract: Low-energy dynamics of Quantum Chromodynamics (QCD) is an important subject for nuclear and hadron physics, but it is a strongly coupled system and difficult to solve. In this situation, symmetry and also anomaly give us an important guide to make a solid conclusion onpossible behaviors of QCD. We find a new discrete anomaly in massless QCD, which says that the baryon number current is anomalously broken under the background gauge field for vector-like flavor symmetry and discrete axial symmetry. To match this anomaly in the chiral-symmetry broken phase, the existence of baryons as Skyrmions is mandatory, and Skyrmion current must show the same anomaly. This is satisfied in the ordinary scenario of chiral symmetry breaking, but not satisfied in an exotic scenario of chiral symmetry breaking proposed by Stern about two decades ago. Since the anomaly matching is applicable even with the sign problem, Stern phase is excluded even for the finite-density QCD at zero temperatures.


12/12/2019 Yuya Tanizaki (NCSU)


Title: Modifying instanton sums in QCD


Abstract: In the path integral formulation, we need to sum up all possible field configurations to define a QFT. If the configuration space is disconnected, we must specify how they should be summed by giving extra data to specify the QFT. In this talk, we try to restrict the possible number of instantons in SU(N) gauge theories, Yang-Mills theory and QCD, and we find out the vacuum structures of them. For consistency with locality, we have to introduce an extra topological degrees of freedom, and the theory acquires the 3-form symmetry. The existence of this 3-form symmetry leads to extra vacua, and moreover it turns out to give an interesting selection rule for the domain-wall excitation/vacuum decay. 



Artan Sheshmani (Harvard CMSA)


Title: Higher rank flag sheaves and Vafa-Witten invariants

Abstract: We study moduli space of holomorphic triples $f: E_{1} \rightarrow E_{2}$, composed of (possibly rank $>1$) torsion-free sheaves $(E_{1}, E_{2})$ and a holomorphic map between them, over a smooth complex projective surface $S$. The triples are equipped with a Schmitt stability condition. We prove that when the Schmitt stability parameter becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute obstruction theory in some cases (depending on Chern character of $E_{1}$). We further generalize our construction to higher-length flags of higher rank sheaves by gluing triple moduli spaces, and extend earlier work, with Gholampur and Yau, where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of flags $E_{1}\rightarrow E_{2}\rightarrow \cdots \rightarrow E_{n}$, where the maps are injective (by stability). There is a connection, by wall-crossing in the master space, developed by Mochizuki, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of any threefold given by a line bundle over the surface, $X :={\rm Tot}(L \rightarrow S)$. The latter DT invariants, when L is the canonical bundle of S, contribute to Vafa-Witten invariants. Joint work with Shing-Tung Yau, arXiv:1911.00124.

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