Lattice Formulation of Supersymmetric Yang-Mills Theories without Fine-Tuning

TL;DR

This paper introduces a lattice formulation for super Yang-Mills theories across various dimensions that preserves supersymmetry in the continuum limit without the need for fine-tuning, leveraging chiral and parity symmetries.

Contribution

It provides a novel lattice approach to formulate super Yang-Mills theories with exact supersymmetry in multiple dimensions without fine-tuning, using the overlap formalism and dimensional reduction.

Findings

Successfully formulated 3D, 4D, 6D, and 10D super Yang-Mills theories on the lattice.

Maintained supersymmetry in the continuum limit through chiral and parity symmetries.

Extended the formulation to theories with simple and extended supersymmetry.

Abstract

We present a lattice formulation which gives super Yang-Mills theories in any dimensions with simple supersymmetry as well as extended supersymmetry in the continuum limit without fine-tuning. We first formulate super Yang-Mills theories with simple supersymmetry in 3,4,6,10 dimensions, incorporating the gluino on the lattice using the overlap formalism. In 4D, exact chiral symmetry forbids gluino mass, which ensures that the continuum limit is supersymmetric without fine-tuning. In 3D, exact parity invariance plays the same role. 6D and 10D thories being anomalous, we formulate them as anomalous chiral gauge theories as they are. Dimensional reduction within lattice formulation is then applied to the theories in 3,4,6 and 10D to obtain super Yang-Mills theories in arbitrary dimensions with either simple or extended supersymmetry.