Speaker
Description
It is difficult to reconcile chiral symmetry with the lattice because of the fermion doubling problem. I start by explaining why simple solutions, that work for the global chiral symmetry of QCD, fail in the case of a chiral gauge theory. I will then introduce the "symmetric mass generation", or SMG, paradigm, which aims to decouple the fermion doublers by introducing judiciously chosen mutli-fermion or fermion-scalar interactions. The main result I will present is a generalization of the Nielsen-Ninomiya "no-go" theorem, which is a theorem about free lattice hamiltonians, to interacting (including SMG) models. The physical reasons why such a generalization exists will be clarified, as well as the conditions of the generalized theorem. This in turn leads to a "check list" that should be addressed in any SMG model if it is to succeed in generating a lattice chiral gauge theory in the continuum limit. As a testbed, I will discuss recent efforts to put on the lattice the so-called 3-4-5-0 chiral Schwinger model. Time permitting, I will also briefly discuss other approaches to the construction of lattice chiral gauge theories that have obtained partial successes, but also have remaining open issues.