Lattice chiral gauge theories - where do we stand?

by Yigal Shamir (Tel Aviv Univ.)

Thursday Feb 26, 2026, 12:00 PM → 1:00 PM Europe/Madrid

C7b/058 - Seminar (IFAE Main Building C7b)

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.