Fermionic anomalies and topological phases on the lattice

by Hersh Singh (Fermilab)

Tuesday 24 Dec 2024, 16:00 → 17:00 Asia/Kolkata

AG (69)

The Standard Model of particle physics has an embarrassing fundamental problem—we cannot formulate it nonperturbatively. This stems from the difficulty of putting a chiral gauge theory on the lattice. The Ginsparg-Wilson (GW) relation, which encodes how anomalous chiral symmetry "optimally" manifests on the lattice, has been pivotal in improving our understanding of this problem. On the other hand, work in condensed matter physics has revealed deep connections between anomalies and topological materials, where anomalous theories can arise at the boundary of topological phases.

In this talk, we will show how the Ginsparg-Wilson relation can be generalized to boundary theories of various topological insulators and superconductors, emphasizing how perturbative and global anomalies arise naturally from the lattice measure. We will also discuss subtleties associated with a Hamiltonian formulation. Addressing these would be crucial for future quantum simulations of any quantum field theory where chiral symmetry plays an important role, such as QCD or the Standard Model.