Momentum space topology in the lattice gauge theory

TL;DR

This paper explores the topological properties of momentum space in lattice gauge theories, introducing invariants that relate to phase transitions and massless particles, with applications to overlap fermions.

Contribution

It formulates a new index theorem connecting topological invariants to phase transition phenomena in lattice gauge theories.

Findings

Topological invariants are defined for gauge theories with a mass gap.

The index theorem links topological jumps to massless particles and unparticles.

Illustration provided using a lattice model with overlap fermions.

Abstract

Momentum space topology of relativistic gauge theory is considered. The topological invariants in momentum space are introduced for the case, when there is the mass gap while the fermion Green functions admit zeros. The index theorem is formulated that relates the number of massless particles and generalized unparticles at the phase transitions to the jumps of the topological invariants. The pattern is illustrated by the lattice model with overlap fermions.