Week 10.04.2023 – 16.04.2023

In this talk I will discuss aspects of global symmetry and their t Hooft anomalies in lattice systems. I will discuss how anomalies are defined and probed using topological defects, which will be applied to both internal and lattice symmetries. The latter arise in systems satisfying Lieb-Schultz-Mattis-type theorems. Using the example of a spin-1/2 XXZ chain, I will also discuss how the continuum limit of a lattice model is properly described in terms of a low-energy theory with topological defects. In particular, I will show that t Hooft anomaly explains a curious size dependence of the ground state lattice momentum in the spin-1/2 XXZ chain.

We propose a (bosonic) worldsheet description of two-dimensional Yang-Mills. We also argue that similar worldsheet actions provide candidate duals to the symmetric product orbifolds for arbitrary seed CFTs.

We will overview some of the recent progress regarding IR dualities across dimensions. In such dualities one engineers the same low energy QFT starting from high energy descriptions in different space-time dimensions. We will review how various strong coupling phenomena can follow from embedding the system of interest in such an across dimensions setup. We will also outline some of the open problems/questions in the field.