Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills

TL;DR

This paper develops a lattice formulation of a mass-deformed 2D N=(8,8) super Yang-Mills theory that preserves some supersymmetry, stabilizes scalar fields, and connects to higher-dimensional theories like N=4 super Yang-Mills.

Contribution

It introduces a mass-deformed lattice model preserving two supercharges, resolving vacuum degeneracy issues, and providing a nonperturbative framework for matrix string theory and higher-dimensional SYM.

Findings

Lattice model free from vacuum degeneracy

Emergence of 4D N=4 SYM around fuzzy spheres

Preliminary 1-loop corrections support soft SUSY breaking scenario

Abstract

We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N=4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N=4 super Yang-Mills on R^4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.