Chiral Determinant as an Overlap of Two Vacua

TL;DR

This paper presents a formalism expressing the chiral fermion effective action as an overlap of two vacua, providing a nonperturbative lattice approach that captures anomalies and the imaginary part of the chiral action.

Contribution

It introduces a lattice transfer matrix formalism for chiral fermions, connecting continuum anomalies with a nonperturbative lattice overlap framework.

Findings

Correct anomaly reproduction in 2D Abelian gauge fields

Nonperturbative definition of the real part of the overlap

Lattice version of the overlap reproduces continuum limits

Abstract

The effective action induced by chiral fermions can be written, formally, as an overlap of two states. These states are the Fock ground states of Hamiltonians for fermions in even dimensional space with opposite sign mass terms coupled to identical static vector potentials. A perturbative analysis of the overlap in the continuum framework produces the correct anomaly for Abelian gauge fields in two dimensions. When a lattice transfer matrix formalism is applied in the direction perpendicular to a domain wall on which chiral fermions live a lattice version of the overlap is obtained. The real part of the overlap is nonperturbatively defined and previous work indicates that the real part of the vacuum polarization tensor in four dimensions has the correct continuum limit for a chiral theory. The phase of the overlap represents the imaginary part of the chiral action and suffers from ambiguities.