Recent progress of lattice and non-lattice super Yang-Mills

TL;DR

This paper discusses recent advances in non-perturbative formulations of supersymmetric Yang-Mills theories, demonstrating the validity of lattice approaches and proposing a new four-dimensional formulation inspired by string theory.

Contribution

It provides new non-perturbative evidence for lattice formulations of supersymmetric theories and introduces a novel four-dimensional approach combining lattice and matrix model techniques.

Findings

Lattice formulations are valid at non-perturbative levels.

Most numerical studies do not fully capture continuum physics.

A new 4D formulation inspired by D-brane dynamics is proposed.

Abstract

We report recent progress of non-perturbative formulation of supersymmetric Yang-Mills. Although lattice formulations of two-dimensional theories which are fine tuning free to all order in perturbation theory are known for almost ten years, however, there were only few evidence for the validity at non-perturbative level. In this talk we argue that most numerical studies so far do not capture the physics in continuum, and add new evidence that lattice formulation works at non-perturbatively. We further point out that, by combining two-dimensional lattice and matrix model techniques inspired by D-brane dynamics in superstring theory, a non-perturbative formulation of the four-dimensional maximally supersymmetric Yang-Mills theory, which is free from the fine tuning at least to all order in perturbation theory, is obtained.