Michael Levin - A lower bound on topological entanglement entropy It is widely believed that (2+1)D gapped phases of matter with anyon excitations have a special pattern of entanglement in their ground state wave function. One attempt to make this intuition precise involves a quantity known as the topological entanglement entropy (TEE). In many systems, the TEE takes a universal value that is directly related to the types of anyon excitations in the corresponding phase. However, this isn’t always true: (finely-tuned) counterexamples have been found where the TEE takes a value different from the one predicted by the anyon theory. These counterexamples call into question the use of the TEE as a diagnostic for detecting anyons. I will discuss a (partial) resolution to this question based on a rigorous lower bound on the TEE.

Carolyn Zhang - Three approaches to anomalies of non-invertible symmetries Anomalies of global symmetries are obstructions to flowing to a gapped, symmetric, non-degenerate phase on any manifold. Non-invertible symmetries, like invertible ones, can also be anomalous, but their anomalies are much less understood. I will describe three different approaches to answering the following question: given the data describing a non-invertible symmetry in $d+1$ spacetime dimensions, how do we detect whether or not the symmetry is anomalous? Each approach has its own strengths and weaknesses. The two approaches that I will focus on involve at least partially constructing the symmetry TFT, which is a corresponding ``inflow" TQFT in $d+2$ spacetime dimensions. I will apply these approaches to detect anomalies of simple examples of non-invertible symmetries.

Anders Sandvik - Decinfined quantum criticality; large-scale simulations and experiments The deconfined quantum-critical point (DQCP) was originally proposed as a generic transition separating antiferromagnetic and singlet patterned phases (valence-bond solids) of 2D quantum magnets. Recent numerical studies instead point to a fine-tuned multi-critical DQCP [1] that is also connected to a gapless spin liquid phase [2]. I will discuss recent (published and unpublished) results of quantum Monte Carlo (QMC) simulations of a class of J-Q models (Heisenberg models with additional multi-spin interactions), showing that there are two charge-0 [under the microscopic O(3)*Z4 symmetry of the models] operators and that the transition can be tuned from strong to very weakly first-order in sign-problem free QMC simulations. This leads to the conjecture that the DQCP is associated with sign problems and cannot be easily studied with QMC simulations. However, I will demonstrate equal scaling dimensions extracted from models with different degrees of first-order behavior, suggesting that universal critical exponents can still be accessed before the flow to a coexistence state (first-order transition) sets in. I will also discuss how SO(5) symmetry is violated when the system flows to the coexistence state and also present results for the entanglement entropy. Time permitting, I will discuss a generalization of the Kibble-Zurek mechanism when performing quantum annealing through the DQCP [3], which supports a duality between the topological defects of the ordered phases. I will also mention a recent experiment in which proximity to a DQCP was detected [4]. [1] B. Zhao, J. Takahashi, and A. W. Sandvik, PRL 125, 257204 (2020). [2] J. Yang, A. W. Sandvik, and L. Wang, PRB 105, L060409 (2022). [3] Y.-R. Shu, S.-K. Jian, A. W. Sandvik, and S. Yin, arXiv:2305.04771. [4] Y. Cui et al., Science 380, 1179 (2023).

Erich Poppitz - Anomalies, tori, and new twists in the gaugino condensate I will describe how recent advances in the understanding of generalized anomalies make it possible to improve and interpret a semiclassical calculation - first attempted in 1984 - of the gaugino condensate in SU(2) super-Yang-Mills theory in the twisted femtouniverse. I will describe the salient points and present some outstanding puzzles to provoke discussion and stimulate further thoughts about semiclassics and contintuity.

Liujun Zou - From quantum anomaly to the classification of quantum phases in quantum materials A central goal of quantum matter physics is to classify quantum phases that can emerge in a quantum material. In this talk, I will argue how the robust properties of a quantum material are encoded in its quantum anomaly, and how this observation can be used to classify quantum phases in this material. As specific examples, I will present some striking predictions of some quantum spin liquids not been envisioned before.

Zechuan Zheng - Bootstrapping the Yang-Mills theory In this talk, we focus on the application of the bootstrap method to Yang-Mills theory. This approach synergistically integrates the Makeenko-Migdal loop equation with the positivity conditions inherent to the associated Hilbert space. Hitherto, its application has been primarily confined to lattice theory with the Wilson action, specifically in the context of the large N limit. We aim to provide a comprehensive overview of these results while also shedding light on the recent advancements within this methodological framework.

Anton Kapustin- Symmetries, anomalies, and the bulk-boundary correspondence ’t Hooft anomalies are obstructions to gauging a global symmetry of a QFT. In one spatial dimension ’t Hooft anomaly of a Lie group symmetry can also be described purely algebraically, without a reference to gauging: it manifests itseld a non-trivial central extension of the current algebra. In higher dimensions, there is no completely satisfactory algebraic reformulation of ’t Hooft anomaly. In this talk, I will argue that such an algebraic reformulation should involve higher-form symmetries. To support this claim I will discuss analogous issues for gapped lattice systems in one dimension higher which are related to QFT via the bulk-boundary correspondence.

Luca Delacretaz - Nonlinear Effective Field Theory of Fermi Liquids Landau's theory of Fermi liquids is a cornerstone of theoretical physics. I will show how to formulate Fermi liquid theory as an effective field theory of bosonic degrees of freedom, using the mathematical formalism of coadjoint orbits. While at the linear level, this theory reduces to existing multidimensional bosonization approaches, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response, such as higher-point functions of currents. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior, and provides a computationally advantageous approach for non-Fermi liquids -- strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions.

Ruben Verresen - Higgs condensates are symmetry-protected topological phases Generalized symmetries have given a re-interpretation of deconfined phases of gauge theories as spontaneous symmetry-breaking (of higher-form symmetries). In this talk we will explore the question: what do these symmetries imply about the Higgs phase? I will argue it is a non-trivial symmetry protected topological (SPT) phase. This gives some new insight into the Fradkin-Shenker phase diagram. Moreover, it recasts superconductors as SPT phases, and supercurrents as Thouless pumps.

Christof Gattringer - 2d lattice field theories at non-zero topological angle In recent years new formulations for gauge fields on the lattice allowed to discretize topological terms such that all symmetries are kept intact. Combined with worldline/worldsheet representations that overcome the complex action problem, this allows one to study topological terms on the lattice. We discuss some recent results for theories with bosonic and fermionic matter in 2-d.

Maria Neuzil - 1-form symmetry vs large N QCD I will show that large N QCD does not have an emergent 1-form symmetry as might be expected from its selection rules. This provides a challenge to a symmetry-based understanding of (approximate) confinement in QCD.

Thomas Dumitrescu - Quark-Hadron Phase Transitions in QCD I will discuss QCD-like theories in 3+1 dimensions with matter in the fundamental representation, which do not admit a sharp characterization of confinement. In modern parlance, they do not have any generalized symmetries that act on loop oder parameters. A closely related piece of standard lore, going back to rigorous lattice results of Fradkin and Shenker, is that such theories can continuously interpolate between the gapped confining and Higgs regimes without encountering a phase transition. I will present simple examples of such theories where one can rigorously show that the confining and Higgs regimes are necessarily separated by a phase transition, because they furnish distinct symmetry-protected topological (SPT) phases. Finally, I will argue that a similar phenomenon takes place in QCD at finite baryon density.

Ho Tat Lam - Modulated Symmetry Protected Topological Phases Modulated symmetries are symmetries that act in a space-dependent manner, such as multipole, exponential, and subsystem symmetries. I will introduce exactly solvable models of topological phases protected by modulated symmetries. Then I will discuss their classifications and construct their response field theories. As modulated symmetries naturally couple to tensor gauge fields, these response field theories can be understood as the generalizations of the Dijkgraaf-Witten twists for tensor gauge theories.

Anatoly Konechny - Cardy's variational ansatz, TCSA and phase structure of 2D QFTs Cardy's variational ansatz approximates vacuum states of perturbed CFTs by a smeared conformal boundary state. The ansatz can be used in conjunction with TCSA numerical data to chart a phase diagram of QFTs obtained by perturbing a given CFT. I will discuss various aspects of using the ansatz for mixed perturbations when several relevant operators are simultaneously switched on. I will illustrate how to use the ansatz and TCSA on the examples of critical and tricritical Ising theories. A general conjecture will be proposed according to which lines or surfaces separating different massive phases are associated with boundary RG flows between the conformal states approximating the vacua.

Ruchira Mishra - Applied nonrelativistic conformal field theory: scattering-length and effective-range corrections to nuclear physics In a range of energy, neutrons are described by the nonrelativistic conformal field theory of unitarity fermions, perturbed by one relevant and an infinite number of irrelevant operators. We develop a formalism which provides a definition of local operators in that nonrelativistic conformal field theory. We compute the scattering-length and effective-range corrections to the two-point functions of primary charge-3 operators. These calculations allow us to find the first corrections to the scale-invariant behaviours of the rate of nuclear reactions with three neutrons in the final state in the regime when the neutrons have small relative momenta.

Ryan Lanzetta - Universal constraints on spin chains from anomalies and conformal bootstrap The Lieb-Schultz-Mattis (LSM) theorem and its generalizations provide criteria for diagnosing mixed ’t Hooft anomalies between spatial and internal symmetries in lattice Hamiltonians. One version of LSM applies to lattice Hamiltonians with translation symmetry and an internal symmetry that is realized projectively at each site. I will introduce various techniques for incorporating a possible IR realization of this kind of mixed anomaly into the conformal bootstrap in (1+1)d, which will allow universal bounds on CFTs with the assumed symmetries and anomalies to be obtained. I will show that, for CFTs with certain "LSM anomalies", there is a universal upper bound on the scaling dimension of the lightest charged operator, both in the bulk and on the boundary in the presence of a maximally symmetric boundary condition.