A Plane Defect in the 3d O(N) Model
2023-12-01 16:30 - 17:30 (America/New_York) | Hybrid
Quantum Matter Seminar
Speaker: Abijith Krishnan (MIT)
Title: A Plane Defect in the 3d O(N) Model
Abstract: It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

Fermi surface symmetric mass generation and its application in nickelate superconductor
2023-12-08 14:30 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint Quantum Matter in Mathematics and Physics & Topological Quantum Matter Seminar
Speaker: Da-Chuan Lu (UCSD)
Title: Fermi surface symmetric mass generation and its application in nickelate superconductor
Abstract: Symmetric mass generation (SMG) is a novel interaction-driven mechanism that generates fermion mass without breaking symmetry, unlike the standard Anderson-Higgs mechanism. SMG can occur in the fermion system without quantum anomalies. In this talk, I will focus on the SMG for the systems with finite fermion density, i.e., the Fermi surface. I will discuss the Fermi surface anomaly and Fermi surface SMG. Lastly, I will talk about its application in the newly found nickelate superconductors, where the superconductivity emerges without a nearby spontaneous symmetry-breaking phase.

When does a three-dimensions Chern-Simons theory have a time reversal symmetry?
2023-12-14 14:30 - 16:00 | Virtual
Speaker: Roman Geiko (UCLA)
Title: When does a three-dimensions Chern-Simons theory have a time reversal symmetry?
In this talk, I will discuss the time reversal invariance of (spin-) Chern-Simons theory in 3 dimensions at both classical and quantum levels. I will show how to obtain a complete classification of Abelian anyons with the time reversal symmetry expressed in terms of the higher Gauss sums. Then, I will comment on the time reversal symmetry of Chern-Simons in the non-Abelian case.

Exact lattice chiral symmetry in 2d gauge theory
2023-12-15 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Aleksey Cherman (UMN)
Title: Exact lattice chiral symmetry in 2d gauge theory
Abstract: Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory. I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

Gauging spacetime inversions
2024-01-26 09:30 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Daniel Harlow (MIT)
Title: Gauging spacetime inversions
Abstract: Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries. In particular this includes CRT symmetry (in even dimensions usually combined with a rotation to become CPT), which in quantum field theory is always a symmetry and seems likely to be a symmetry of quantum gravity as well. I’ll discuss what it means to gauge a spacetime inversion symmetry, and explain some of the more unusual consequences of doing this. In particular I’ll argue that the gauging of CRT is automatically implemented by the sum over topologies in the Euclidean gravity path integral, that in a closed universe the Hilbert space of quantum gravity must be a real vector space, and that in Lorentzian signature manifolds which are not time-orientable must be included as valid configurations of the theory.

Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions
2024-02-02 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Anurag Anshu (Harvard)
Title: Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions
Abstract: At the heart of the theory of NP completeness lies a mapping from classical circuits to constraint satisfaction problems (classical local Hamiltonians).
The quantum analogue of this is the remarkable history state construction of Kitaev (building upon Feynman’s work). This talk will provide an introduction to this mapping and its crucial role in bridging quantum computer science and quantum many-body physics research. Then, we will describe a new mapping using tensor networks and quantum fault tolerance (https://arxiv.org/abs/2309.16475). Time permitting, we will discuss the relevance of this mapping to the quantum PCP conjecture.

Flavor hierarchy from smooth confinement & Towards a complete classification of 6d supergravities
2024-02-06 16:00 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Yuta Hamada (KEK, Tsukuba)
Title: Flavor hierarchy from smooth confinement & Towards a complete classification of 6d supergravities
Abstract: The talk consists of two independent parts. In the first part, I will talk about a new model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement. The smallness of the first- and second-family fermion masses is explained by the exponential hierarchy via dimensional transmutation. In the second part, I will talk about a classification of 6D supergravities. We make progress towards a complete classification of 6D supergravities with minimal supersymmetry and non-abelian gauge group.
References – arXiv: 2209.15244, 2309.15152, 2311.00868

Quantum Algorithms to Recognize Phases of Matter and Exactly Solvable 2D Models with Anomalous Entanglement Entropy
2024-02-09 09:30 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Soonwon Choi (MIT)
Title: Quantum Algorithms to Recognize Phases of Matter and Exactly Solvable 2D Models with Anomalous Entanglement Entropy
Abstract: In this talk, I will report my two recent results at the intersection of quantum information and strongly interacting phases of matters.
In the first half of the talk, we describe exact quantum algorithms that recognize a class of 1D gapped phases, namely symmetry protected topological phases or spontaneous symmetry breaking phases protected by abelian internal symmetry. The key idea is to observe the conceptual similarity between renormalization group (RG) flow and error correction, and to implement the latter as unitary circuits emulating the RG flow. Our algorithm guarantees faithful recognition of a target phase with a small number of input quantum state samples.
In the second half, we present a class of 2D Hamiltonians, where the exact ground state wavefunctions can be exactly evaluated and shown to exhibit anomalous entanglement properties. One class of our models exhibit area-law scaling entanglement entropy, but this is mostly due to non-local correlation: one finds that the topological entanglement entropy also scales with the size of subsystem choices. By making simple modifications, we can also devise 2D models with volume-law scaling bipartite entanglement entropy. Our results can be understood as a generation of the 1D Motzkin model to 2D systems.
Based on work done with Ethan Lake and Shankar Balasubramanian
https://arxiv.org/abs/2211.09803
https://arxiv.org/abs/2305.07028

Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
2024-02-14 16:00 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Sen Hu (Shanghai Institute for Mathematics and Interdisciplinary Study)
Title: Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
Abstract: In this talk we discuss the algebra of quantum observables of the Chern-Simons matrix model which was originally proposed by Susskind and Polychronakos to describe electrons in fractional quantum Hall effects. We establish the commutation relations for its generators and study the large N limit of its representation. We show that the large N limit algebra is isomorphic to the uniform in N algebra studied by Costello, which is conjecturally isomorphic to the deformed double current algebra studied by Guay. Under appropriate scaling limit, we show that the large N limit algebra degenerates to a Lie algebra which admits a surjective map to the affine Lie algebra of u(p). This leads to a complete proof of the large N emergence of the u(p) current algebra as proposed by Dorey, Tong and Turner. This also suggests a rigorous derivation of edge excitation of a fractional quantum Hall droplet. This is a joint work with Si Li, Dongheng Ye and Yehao Zhou (arXiv: 2308.14046).

Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
2024-02-16 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Susanne Yelin (Harvard)
Title: Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
Abstract: Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. We introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral and other relevant chemical information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials.

Spontaneously Broken (-1)-form symmetries
2024-02-23 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Motoo Suzuki (Harvard)
Title: Spontaneously Broken (-1)-form symmetries
Abstract: Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to (−1)-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field θ, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. We discuss how known solutions to the problem are unified in this framework and explore some, so far unsuccessful, attempts to find new solutions. I will also talk about our ongoing work on the explicit breaking by monopoles.

A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
2024-03-08 09:00 - 10:00 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Semeon Valgushev (Iowa State University)
Title: A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
Abstract: Many properties of quantum field theories can be understood with the help of classical numerical methods. Yet there are several outstanding problems — most remarkably the behaviour of nuclear matter at finite density and out-of-equilibrium real-time dynamics — that require the use of quantum algorithms. We present a simple yet physically rich toy model of QCD/nuclear matter at finite density, termed “QZD”, where Z stands for Z(3) gauge theory coupled to Nf = 3 fermion flavors, suitable for simulation on near-term quantum devices. We study it using tensor networks and find that in weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.

Cluster state as a noninvertible SPT phase
2024-03-13 10:00 - 12:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Shu-Heng Shao (SUNY Stony Brook)
Title: Cluster state as a noninvertible SPT phase

Abstract: We will point out a non-invertible symmetry of the ordinary 1+1d Z2xZ2 cluster Hamiltonian. Therefore, the cluster state can be viewed as a non-invertible SPT phase under this fusion category symmetry, which is Rep(D8). We furthermore find two new stabilizer states that are distinct from the cluster state as Rep(D8) SPT phases, but identical as Z2xZ2 SPT phases. Finally, we discuss the degenerate edge modes at the interfaces between these three Rep(D8) SPT phases.

Monopoles, scattering, generalized symmetries
2024-03-15 10:00 - 11:30 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Diego Delmastro (Simons Center for Geometry and Physics)
Title: Monopoles, scattering, generalized symmetries

Abstract: Gauge theory is a very mature subject by now. Surprisingly, some of its symmetries have only been properly understood in the last couple of years. Specifically, such theories typically have a very rich set of symmetries, involving modern notions such as higher-form symmetries, higher-group symmetries, and categorical symmetries. A proper understanding of these generalized symmetries is not really crucial if we are interested in scattering processes involvingfundamental particles only, but it does become quite essential if we want to add monopoles into the mix. In this talk I will review where these generalized symmetries come from, and how they impose constraints on scattering amplitudes of elementary particles against heavy monopoles. This will allow us to resolve a decades-old puzzle concerning such processes, where incoming electrons appear to become fractional particles after the scattering event.

Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem
2024-03-22 09:00 - 10:30 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Sungwoo Hong, Korea Advanced Institute of Science and Technology (KAIST)
Title: Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem
Abstract: In this talk, I will discuss a new solution to the strong CP problem, one of the most important and challenging problems, of the Standard Model (SM) based on the generalized global symmetry. To this end, I will first show that there exist non-invertible chiral symmetries acting on quark fields once the SM is extended with gauged quark flavor symmetry. Interestingly enough, such symmetries, which we named them as “non-invertible Peccei-Quinn symmetries”, exist only because the SM has the same number of generations as colors, yet another feature that deserves a fundamental explanation. Then I discuss how these new generalized symmetries set the down Yukawa to be exactly zero and lead to a massless quark solution to the strong CP problem. Completion of the solution requires (i) generation of down quark Yukawas to be consistent with both observed quark mass spectrum and mixings and (ii) generation of O(1) CP violating phase called CKM phase, crucially without destabilizing our solution to the strong CP problem. I will discuss that these rather non-trivial tasks can be achieved by a UV completion in an SU(9) quark color-flavor unification.

Discrete geometry and the modular bootstrap
2024-04-05 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Henry Cohn (MIT and Microsoft)
Title: Discrete geometry and the modular bootstrap
Abstract: In this talk, I’ll discuss the remarkable connections between the modular bootstrap and sphere packing or ground state problems discovered by Hartman, Mazáč, and Rastelli in 2019, with a focus on opportunities for further progress.

Fusion Rule Measurement in a Topological Qubit
2024-04-19 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Chetan Nayak, Microsoft and UCSB
Title: Fusion Rule Measurement in a Topological Qubit

What Observables are Safe to Calculate?
2024-04-26 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Jesse Thaler, MIT
Title: What Observables are Safe to Calculate?
Abstract: In collider physics, perturbative quantum field theory is the workhorse framework for computing theoretical predictions to compare to experimental measurements. An observable is called “safe” if its cross section can be predicted order-by-order in perturbation theory with controlled non-perturbative corrections. In this talk, I show that naive definitions of “safety” are inadequate to determine which observable are perturbatively calculable. I then argue for a more refined definition of safety based on principles from optimal transport theory.

From quantum Hall to Hubbard physics in twisted bilayer graphene
2024-05-10 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Eslam Khalaf (Harvard)
Title: From quantum Hall to Hubbard physics in twisted bilayer graphene

Abstract: Early on it was noticed that twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: Hubbard physics and quantum Hall physics. On the one hand, TBG hosts flat topological Landau-level-like bands which realize quantum anomalous Hall states and orbital ferromagnetism under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show experimental signs of fluctuating magnetism, and unconventional superconductivty; all characteristics of Hubbard-model-like physics. The emergence of fluctuating moments is particularly surprising, as localized Wannier states do not exist in topological bands. I will discuss a phenomenological model for the flat bands in TBG that centers the concentration of charge density and, relatedly, the concentration of Berry flux. The bands obtained have excellent quantitative agreement with the Bistritzer-Macdonald model for realistic parameters. I will show that, rather remarkably, the model hosts decoupled flavor moments which despite being only power-law delocalized with infinite localization length, have parametrically small overlap with each other. I will show how this unifies many of the observations in TBG and leads to a novel Mott semimetal phase for intermediate temperatures where moments are thermally disordered but charge fluctuations are mostly frozen.

Improving Mean-Field Theory for Quantum Magnets
2024-05-13 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Junyi Zhang, Johns Hopkins University
Title: Improving Mean-Field Theory for Quantum Magnets
Abstract: Frustrated magnets have garnered significant attention because of their potential to host exotic spin liquids, while many real material candidates exhibit magnetic orders. Due to their proximity to spin liquid phases, the semiclassical descriptions of these magnetic orders often fall short in capturing their intricate quantum behaviors. In this talk, I will introduce an improved mean-field method, named density-matrix mean-field theory (DMMFT), for these quantum magnets. Using local reduced density matrix, DMMFT can systematically incorporate the quantum fluctuations beyond conventional mean-field theories. Notably, it not only quantitatively evaluates the renormalization of order parameters induced by quantum fluctuations but also has the capability to detect the topological order of quantum phases. DMMFT offers an efficient approach to explore phases displaying unconventional quantum orders, particularly beneficial for investigating frustrated spin systems in high spatial dimensions.
Ref: https://arxiv.org/abs/2401.06236

Love and Naturalness
2024-05-17 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Mikhail Ivanov (MIT)
Title: Love and Naturalness
Abstract: Recent progress in gravitational wave astronomy has spurred the development of efficient tools to describe gravitational binary dynamics. One such tool is classical worldline effective field theory (EFT). In the first part of my talk, I will show how to use this EFT for systematic studies of tidal heating and deformations (Love numbers) of compact objects. I will present a gauge-invariant definition of Love numbers and show how to extract them in a coordinate-independent way from scattering amplitudes of the gravitational Raman process. I will show that the worldline EFT exhibits strong fine-tuning when applied to black holes. This gives rise to a naturalness paradox associated with the vanishing of black hole static Love numbers. In the second part of my talk, I will present a new symmetry of black holes (Love symmetry) that elegantly resolves this paradox. The Love symmetry is tightly connected to isometries of extremal black holes that appear in many holographic constructions. It also provides a curious example of IR/UV mixing, which may give insights for other hierarchy problems.

Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
2024-06-07 14:30 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Arkya Chatterjee (MIT)
Title: Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
Abstract: Non-invertible symmetries are often emergent at low-energies in gapless states of quantum matter. It is useful to construct lattice models that have these as exact symmetries in order to provide a UV-complete setting in which they are well-controlled. To that end, we propose to study one-dimensional Hamiltonians defined on tensor product Hilbert spaces with finite on-site dimension — referred to as “spin chains” in short — with exact non-invertible symmetries. We focus on two concrete examples: a spin chain with (invertible) S_3 symmetry and one with (non-invertible) Rep(S_3) symmetry. These models are largely analytically tractable and demonstrate all spontaneous symmetry breaking (SSB) phases of these symmetries. With the aid of tensor network algorithms, we systematically study the phase transitions between these SSB phases. Both models possess (intrinsically) non-invertible self-duality symmetries, for which we provide sequential circuit implementations. On the self-dual manifold in parameter space, we discover an incommensurate gapless phase with an anomalous U(1) symmetry which emanates from lattice translation.

Landscape of Tensor Network States Preparable from Measurement
2024-06-21 14:00 - 15:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Rahul Sahay (Harvard)

Title: Landscape of Tensor Network States Preparable from Measurement

Abstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk, we go beyond this, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. In 1D, a complete framework is developed for the case where a single round of measurements is the only entangling operation. Specifically, we completely classify the space of 1D preparable quantum states (forming a strict subset of all matrix product states), and characterize their physical constraints. In doing so, we find an intriguing physical trade-off between the richness of the preparable entanglement spectrum and correlation functions, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover, our classification enables one to search for and engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. We conclude by charting out generalizations, such as higher dimensional examples, considering multiple rounds of measurements, and implementing matrix product operators. At a high level, our work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter, away from their fixed points, in quantum devices. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].

Instanton in Lattice QCD from Higher Categories and Higher Anafunctors
2024-08-28 14:00 - 15:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Jing-Yuan Chen, Tsinghua University
Title: Instanton in Lattice QCD from Higher Categories and Higher Anafunctors

Abstract: Putting continuum QFT (not just TQFT) on the lattice is important for both fundamental understandings and practical numerics. The traditional way of doing so, based on simple intuitions, however, does not admit natural definitions for general topological operators of continuous-valued fields—one such example is the long standing problem in lattice QCD of lacking a natural definition for Yang-Mills instantons.
In this talk, I will explain a more systematic way to relate continuum and lattice QFT, based on higher categories and higher anafunctors, so that the topological operators in the continuum can be naturally defined on the lattice. The idea, though formulated formally, is physically very intuitive—we want to effectively capture the different possibilities of how a lattice field may interpolate into the continuum, so the higher categories that are employed to study higher homotopy theory should be naturally involved. Via this formalism, we resolve the long-standing problem of defining instanton (as well as Chern-Simons term) in lattice Yang-Mills theory, in terms of multiplicative bundle gerbes. Moreover, when the fields become discrete, our formalism can recover the Dijkgraaf-Witten and Turaev-Viro theory, so we hope this formalism to be a good starting point towards (in the very long term) a comprehensive categorical understanding of QFT that encompass both continuous and discrete degrees of freedom, applicable both to IR and to UV.

Classification and Construction of crystalline topological superconductors and insulators in interacting fermion systems
2024-09-20 14:00 - 15:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Zhengcheng Gu, Chinese University of Hong Kong
Title: Classification and construction of crystalline topological superconductors and insulators in interacting fermion systems
Abstract: The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide us great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this talk, I will discuss how to construct and classify crystalline topological superconductors (TSC) and topological insulators (TI) in interacting fermion systems. I will also discuss the relationship between internal symmetry protected SPT phases and crystalline symmetry protected SPT Phases.

Dolbeault Virasoro algebra and M5 branes
2024-10-11 09:00 - 10:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Brian Williams, Boston University
Title: Dolbeault Virasoro algebra and M5 branes
Abstract: The worldvolume theory on a stack of M5 branes in M-theory is superconformal. We propose a conjecture that in the holomorphic twist of the theory on a stack of M5 branes an infinite-dimensional enhancement of the (twisted) superconformal algebra is a symmetry. This algebra is closely related to the exceptional infinite-dimensional Lie superalgebra called E(3|6). We show that under the usual AGT correspondence this enhanced algebra degenerates to the Virasoro algebra at a particular central charge.
