Speaker: Hersh Singh (Fermilab)

Title: Fermionic anomalies and topological phases on the lattice: Ginsparg-Wilson relation and its generalizations

Short Bio: Hersh Singh is a postdoctoral researcher in theoretical physics at Fermilab, where he is the Fermilab Quantum Theory Fellow. His research focuses on high-energy physics, with an emphasis on using lattice quantum field theory techniques and the prospect of using quantum computing to improve our understanding of nature at a fundamental level. Prior to Fermilab, Hersh held a postdoctoral position at the InQubator for Quantum Simulation (IQuS) and the Institute for Nuclear Theory (INT) at the University of Washington, Seattle. He earned his Ph.D. in Physics from Duke University, specializing in lattice and effective field theories, and holds Bachelor’s and Master’s degrees in Electrical Engineering from Indian Institute of Technology Madras.

Abstract: The Standard Model of particle physics has a problem -- we cannot formulate it nonperturbatively. This comes from the difficulty of putting a chiral gauge theory on the lattice. One of the important developments motivated by this question is the Ginsparg-Wilson (GW) relation, which encodes how the anomalous chiral symmetry optimally manifests on the lattice.

On the other hand, developments in condensed matter physics have uncovered a deep connection between anomalies and topological phases. Domain-wall fermions used in lattice QCD simulations can be understood as a special case of this. Since domain-wall fermions are a solution to the GW equation, one may wonder -- can the GW relation be generalized to other topological phases? In this talk, we will review the story of chiral fermions on the lattice and the importance of the Ginsparg-Wilson relation. We will then discuss how it can be generalized to boundary theories of various classes of topological insulators and superconductors. Interestingly, perturbative and even some global anomalies (à la Witten) show up in this formalism in an elementary fashion from the Jacobian of the fermionic measure.