A solution to the fermion doubling problem for supersymmetric theories on the transverse lattice

TL;DR

This paper addresses the fermion doubling problem in lattice field theories, demonstrating that the Supersymmetric Discrete Light Cone Quantization (SDLCQ) approach avoids species doubling unlike standard formulations.

Contribution

The paper introduces a supersymmetric transverse lattice formulation that eliminates species doubling, overcoming limitations of traditional lattice methods.

Findings

SDLCQ formulation avoids species doubling

Standard Lagrangian transverse lattice exhibits species doubling

Supersymmetry plays a key role in eliminating doubling

Abstract

Species doubling is a problem that infects most numerical methods that use a spatial lattice. An understanding of species doubling can be found in the Nielsen-Ninomiya theorem which gives a set of conditions that require species doubling. The transverse lattice approach to solving field theories, which has at least one spatial lattice, fails one of the conditions of the Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the standard Lagrangian formulation of the transverse lattice. We will show that the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the transverse lattice does not have species doubling.