Renormalization of Matter Field Theories on the Lattice and the Flow Equation

TL;DR

This paper presents a simplified proof of the renormalizability of certain matter field theories on the lattice using the Wilson flow equation, including $$ and Yukawa theories, and discusses staggered fermions with minimal doubling.

Contribution

It introduces a new, simpler proof of lattice matter field theory renormalizability using the Polchinski approach and extends results to staggered fermions with minimal doubling.

Findings

Proves renormalizability of $$ and Yukawa theories on the lattice.

Demonstrates renormalizability of a chiral sigma model with exact chiral symmetry.

Uses Wilson flow equation for a more straightforward renormalization proof.

Abstract

We give a new proof of the renormalizability of a class of matter field theories on a space-time lattice; in particular we consider $\phi^4$ and massive Yukawa theories with Wilson fermions. We use the Polchinski approach to renormalization, which is based on the Wilson flow equation; this approach is substantially simpler than the BPHZ method, applied to the lattice by Reisz. We discuss matter theories with staggered fermions. In particular we analyse a simple kind of staggered fermions with minimal doubling, using which we prove the renormalizability of a chiral sigma model with exact chiral symmetry on the lattice.