Monday, 18 January 2021

Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems, which has proven crucial to the study of quantum chromodynamics among many other theories. Lattice investigations of supersymmetric field theories have a long history but often struggle due to the interplay of supersymmetry with the lattice discretization of space-time. I will review these issues and recent progress overcoming them, including both pedagogical background as well as discussions of ongoing research and promising directions for future work. Particular focus will be on maximally supersymmetric Yang--Mills theories that play important roles in holography.

I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the models yield a set of sixteen massless Majorana or equivalently Weyl fermions in agreement with results from condensed matter physics and arguments rooted in the Dai-Freed theorem.

**Study Material: **Arxiv papers and references therein 2010.02290, 2101.01026 may prove useful.

Study Materials:

The talk is mainly based on the preprint:

https://arxiv.org/pdf/2012.02153.pdf

Other related useful references are:

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.054505

https://www.sciencedirect.com/science/article/abs/pii/055032139390044P?via%3Dihub

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.75.1891

https://www.sciencedirect.com/science/article/abs/pii/055032139190298C?via%3Dihub

Tuesday, 19 January 2021

In order to investigate nonperturbative dynamics of superstring theory, it is important to use a nonperturbative formulation like lattice gauge theory in the case of quantum field theory. The IKKT matrix model is a promising candidate for such a formulation, and its numerical studies revealed interesting real-time dynamics suggesting the birth of our Universe. I present some new results from complex Langevin simulations used to overcome the sign problem, which suggest an interesting phase diagram with respect to the Wick rotation parameters for the worldsheet and the target space.

Wednesday, 20 January 2021

We propose a novel tensor renormalization group method which is applicable to any dimensional lattice field theory. In this method, the RG is defined on a tensor network made only of rank-3 tensors. We test it in the 3d Ising model and find that the computational cost drastically reduces.

As the 2020 Nobel Prize in Physics made manifest, black hole formation and singularities play a central role in our current understanding of classical gravity in the framework of general relativity. One of the most important open questions in this area is whether, in general, singularities are hidden inside black holes. This question goes under the name of the Weak Cosmic Censorship Conjecture. In this talk, I will review the current status of this conjecture, both in asymptotically flat spaces and in AdS. Determining whether singularities can be accessible to external far away observers is important for the perdictivity of general relativity as a classical theory of gravity and for the possibility of observing Planck scale physics.

**Study Materials:**

- D. Christodoulou, “On the global initial value problem and the issue of singularities”, Class. Quantum Gravity 16 (1999) A23-A35
- L. Lehner and F. Pretorius, ``Final state of Gregory\textendash{}Laflamme instability,’' [arXiv:1106.5184 [gr-qc]].
- P. Figueras, M. Kunesch and S. Tunyasuvunakool, ``End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture,’' Phys. Rev. Lett. \textbf{116} (2016) no.7, 071102 [arXiv:1512.04532 [hep-th]].
- P. Figueras, M. Kunesch, L. Lehner and S. Tunyasuvunakool, ``End Point of the Ultraspinning Instability and Violation of Cosmic Censorship,’' Phys. Rev. Lett. \textbf{118} (2017) no.15, 151103 [arXiv:1702.01755 [hep-th]].
- T. Crisford and J. E. Santos, ``Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti\textendash{}de Sitter Space,'' Phys. Rev. Lett. \textbf{118} (2017) no.18, 181101 [arXiv:1702.05490 [hep-th]].
- T. Crisford, G. T. Horowitz and J. E. Santos, ``Testing the Weak Gravity - Cosmic Censorship Connection,’' Phys. Rev. D \textbf{97} (2018) no.6, 066005 [arXiv:1709.07880 [hep-th]].
- P. Bizon and A. Rostworowski, ``On weakly turbulent instability of anti-de Sitter space,’' Phys. Rev. Lett. \textbf{107} (2011), 031102 [arXiv:1104.3702 [gr-qc]].
- P. M. Chesler and D. A. Lowe, ``Nonlinear Evolution of the AdS$_4$ Superradiant Instability,’' Phys. Rev. Lett. \textbf{122} (2019) no.18, 181101 [arXiv:1801.09711 [gr-qc]].

Thursday, 21 January 2021

Holographic cosmology is a new framework for the very early universe, the period usually associated with inflation. In this framework the early Universe is described by a three dimensional QFT, cosmological evolution is mapped to inverse RG flow and the computation of cosmological observables to the computation of correlation of function of the energy momentum tensor of the dual QFT. In this talk I provide an introduction to holographic cosmology and then discuss how lattice QFT may be used to compute the compute the relevant QFT observables. In particular, I will discuss the IR structure of the dual QFT, which is linked to the question of the resolution of the initial singularity in cosmology, and how to properly define the energy momentum tensor on the lattice.

**Study Materials:**

The talk will be based on 2009.14768, 2009.14767

Useful literature on holographic cosmology.

Minimal introduction: Introduction and section II of 1703.05385

More complete introductory study material: 0907.5542, 1001.2007, 1607.04878, 1703.05385, 1904.05821

Friday, 22 January 2021

I will describe the quantum gravity in the lab program and argue that it offers the possibility of using quantum simulators and quantum computers to study the non-perturbative dynamics of quantum gravity in so far inaccessible regimes. Moreover, even if such simulations are still many years away, I will argue that there are valuable lessons to be learned from asking if and how such simulations can be carried in principle. As a concrete example, I will discuss simulations of traversable wormholes and the notion of teleportation by size.

**Reference**: https://arxiv.org/abs/1911.06314

We study a class of gauge theories whose gauge group is semi-direct product of a continuous abelian $U(1)^{N-1}$ and discrete non-abelian gauge groups, such as permutation group $S_N$. We call this class as semi-abelian theories. Unlike other known calculable models, such as Polyakov model on $R^3$, Seiberg-Witten theory on $R^4$ and QCD(adj) $R^3 \times S^1$ where $S_N$ part of gauge structure is Higgsed, and this pervades the physics of the theory, in the semi-abelian theory, $S_N$ is not Higgsed. Mass gaps and string tensions are calculable in the monopole-gas description, and receive equal contributions from monopoles associated with the entire $SU(N)$ root system, unlike theories like the Polyakov model where only simple roots contribute at leading order.

Even though the center symmetry of the semi-Abelian gauge theory is given by $Z_N$, we observe that the string tensions do not obey the $N$-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of $U(1)^{N-1}$ one-form symmetry in the original Abelian lattice theory.

When adding charged particles corresponding to $W$-bosons, such non-invertible symmetries are explicitly broken so that the $N$-ality rule should emerge in the deep infrared regime. We expect that non-invertible symmetry plays a prominent role both in Yang-Mills theory and QCD with fundamental fermions.

**Reference Material:** LINK