Introductions and Greetings A brief session to meet and greet some early-bird participants and test the equipment and the recording. Feel free to pup up and say hello before the talk starts.

Slava Rychkov: Renormalization group transformations without truncations

• Slava Rychkov

Can one implement a Wilsonian renormalization group transformation without any truncation, or with a rigorous control of error caused by truncation? I will speak about a few known cases where this has been achieved. I will contrast field-theoretic RG, Wilson-Kadanoff lattice RG, and tensor network RG. In particular I will present a recent proof of convergence of tensor network RG to the high-temperature fixed point (arXiv:2107.11464, joint work with Tom Kennedy). This is the first step towards controlling nontrivial fixed points via computer-assisted techniques. YouTube link: https://www.youtube.com/watch?v=N3MPjNCdutY

Rychkov Discussion

Dam T Son: Paths to the QFT of the fractional quantum Hall effect

• Dam T Son

We discuss the constraints placed by the symmetries of the microscopic theory on the low-energy effective field theory of the fractional quantum Hall effect. The symmetries that we will consider are particle-hole conjugations, volume-preserving diffeomorphism, and a noncommutative gauge symmetry. We will show how these symmetries can be implemented in effective field theory. YouTube link: https://www.youtube.com/watch?v=qSAa_C1UvyA

Adam Nahum: Self-dual criticality in the Z2 gauge-Higgs model in three dimensions

• Adam Nahum

The simplest topologically ordered phase in 2+1D is the deconfined phase of Z2 gauge theory. This phase permits a duality that exchanges electric and magnetic excitations (“e” and “m” particles). In the simplest lattice gauge theory formulation, there is a self-dual line in the space of gauge and matter couplings. Away from the self-dual line, there are phase transitions out of the deconfined phase (the Higgs and confinement transitions) that are well understood. But the phase transition on the self dual line is still mysterious, and -- if continuous -- may be the simplest critical point for which we still lack a useful continuum field theory description. After reviewing applications of this model to quantum and classical statistical mechanics, I will describe Monte Carlo results for a wide range of observables at the self-dual transition. The results indicate that it is a novel continuous transition. If time permits I will briefly mention a connection between ``geometrical’’ (percolation) observables in the gauge-Higgs model and its emergent one-form symmetries, as well as some extensions of the model. Work with Andres Somoza and Pablo Serna (https://arxiv.org/abs/2012.15845).

Son/Nahum Discussion

Xie Chen: From quantum hard drive to foliated manifold

• Xie Chen

One major open problem in quantum information theory is how to build a quantum hard drive, i.e. a quantum mechanical system that can store quantum information reliably for a very long time without active error correction. No completely satisfying solution to this problem has been found, but in the search for possibilities a whole new class of quantum many-body models have been discovered with exotic properties that have never been seen before. This new class of models, dubbed the “fracton” models, host point excitations that cannot move freely, have robust ground state degeneracy that increases with system size, and have unusually slow thermalization dynamics even in the absence of any disorder. In this talk, I will introduce some of the most important fracton models and present a systematic framework for characterizing their universal properties. By realizing that the model properties depend on the foliation structure of the underlying manifold, we are able to reveal the hidden equivalence relation between many seemingly different models and identify the direction of search for new nontrivial features. YouTube link: https://www.youtube.com/watch?v=aqptSyKI8Bo

Yuya Tanizaki: Confinement and chiral symmetry breaking of 4d QCD-like theories with 2-torus compactification

• Yuya Tanizaki

I will talk my on-going and preliminary work about 4d gauge theories with 2-torus compactification. By inserting a suitable background gauge field along the torus, the remnant 2-dimensional effective theory shares the same 't Hooft anomaly with the uncompactified 4d theory. As a result, if both theories show confinement, then the anomaly requires fractional theta dependence or chiral symmetry breaking for 2d compactified theory, which are key low-energy features of 4d QCD-like theories. I also argue that confinement of 2d compactified theory is quite reasonable according to semi-classical analysis. YouTube link: https://www.youtube.com/watch?v=DaAPlYfOxSQ

Tanizaki Discussion

David Tong: Comments on Symmetric Mass Generation

• David Tong

Symmetric mass generation is the name given to a mechanism for gapping fermions while preserving a chiral, but necessarily non-anomalous, symmetry. I'll explain how to do this, with emphasis on possible applications to putting chiral gauge theories on the lattice. YouTube link: https://www.youtube.com/watch?v=3woznvM5-iY

Ian Affleck: 1) The Majorana-Hubbard Model 2) Generalizing the Haldane conjecture to SU(n) 1) A superconducting layer in a transverse magnetic field on top of a topological insulator is predicted to have a Majorana mode at the centre of each vortex. This has been verified by experiments. We study both hopping terms between the Majorana modes and also interaction terms. The hopping terms can be tuned to zero by adjusting the chemical potential of the topological insulator so that the ratio of interaction strength to hopping term can be tuned to infinity. We consider the shortest possible range interactions, which we call the Majorana-Hubbard Model. We study the phase diagram of this model in one dimension, in the two dimensional square lattice and two dimensional triangular lattice. 2) In 1981, Haldane predicted that half-integer antiferromagnetic chains are gapless while integer antiferromagnetic chain are gapped. We extend this conjecture to SU(n) chains which may be realized in cold atom experiments. YouTube link: https://www.youtube.com/watch?v=D6G-KN9HIXM

Tong Discussion

Uwe-Jens Wiese: From Quantum Link Models to D-Theory: A Discrete Approach to Gauge Theories

• Uwe-Jens Wiese

Quantum link models provide an extension of Wilson's lattice gauge theory with a finite-dimensional link Hilbert space. Quantum links are discrete quantum variables endowed with an exact continuous local symmetry. For example, an Abelian U(1) quantum link model is formulated in terms of quantum spins residing in a representation of SU(2). Non-Abelian U(N), SO(N), or SP(N) quantum links are generalized quantum spins residing in an embedding algebra SU(2N), SO(2N), or Sp(2N), respectively. On the one hand, quantum link models possess qualitatively new "crystalline" or "nematic" confined phases with spontaneously broken lattice translation or rotation symmetry. On the other hand, they provide an alternative regularization of asymptotically free continuum theories including CP(N-1) models and QCD. The continuum limit is then reached in the framework of D-theory, in which discrete variables undergo dimensional reduction. In this way, (1+1)-d CP(N-1) models arise from the dimensional reduction of (2+1)-d SU(N) quantum spin ladders with massless Goldstone bosons, while (3+1)-d QCD emerges from a (4+1)-d Coulomb phase with massless gluons. Quarks arise naturally as domain wall fermions. Quantum link models provide a formulation of gauge theories with a minimal number of quantum degrees of freedom, which makes them ideally suited for resource efficient quantum simulation and computation experiments. YouTube link: https://www.youtube.com/watch?v=6jJumOGBX9k

Wiese Discussion

Sakura Schäfer-Nameki: Generalized Symmetry Structures QFTs

• Sakura Schäfer-Nameki

I will give an overview of recent advances in generalized symmetries, such as higher form symmetries in QFT. The focus will be on supersymmetric QFTs, where higher form symmetries are known to play an important role in constraining the IR dynamnics of N=1 theories. I will review these basics, and discuss recent extensions to more exotic QFTs arising in string theory, both in 4d and in 5d, which have not necessarily a UV Lagrangian description. YouTube link: https://www.youtube.com/watch?v=MLKRedQvfxQ

Chen/Affleck Discussion

Schäfer-Nameki discussion

Fakher Assad: Quantum Monte Carlo simulations of Dirac systems and continuum field theories

• Fakher Assad

YouTube link: https://www.youtube.com/watch?v=aylI1RFXwgY

Assad Discussion

Ribhu Kaul: 1) Condensed matter paths to QFT, 2) Symmetries in designer models of spins and fermions: Lattice and the Continuum

• Ribhu Kaul

YouTube link: https://www.youtube.com/watch?v=Yvin10a7ANQ