An illustration of chiral fermions on a 1+1 dimensional lattice

TL;DR

This paper investigates chiral fermions on a 1+1 dimensional lattice, demonstrating how strong interactions and anomaly cancellation preserve chiral symmetry and zero modes, with detailed analysis of energy gaps and bound states.

Contribution

It provides an exact analysis of an anomaly-free chiral model on a 1+1D lattice, illustrating the behavior of energy gaps and zero modes under strong interactions.

Findings

High-momentum states develop a negative energy-gap, preserving chiral symmetry.

Bound states and constituents fill the same energy level, maintaining anomaly cancellation.

Zero-energy modes are unaffected by gauge field fluctuations due to anomaly considerations.

Abstract

The vectorlike doubling of low-energy excitations is in fact a natural consequence of the pair-production around the zero-energy (E=0) due to the quantum field fluctuations of the lattice regularized vacuum. On the 1+1 dimensional lattice, we study an anomaly-free chiral model (11112) of four left-movers and one right-mover with strong interactions. Exact computations of relevant S-matrices illustrate that for high-momentum states, a negative energy-gap (E<0) develops; the bound state and its constituents, which have the same quantum numbers but opposite chiralities, fill the same energy-state so that chiral symmetries are preserved; for low-momentum states, the negative energy-gap vanishes and the bound state dissolves into its constituents near zero energy. As a consequence of the gauge-anomaly cancellation and the index theorem for flavor-singlet anomalies, the net number of zero-modes pushed down into and pumped out from the zero-energy level by the gauge field is zero.