Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

TL;DR

This paper develops a non-perturbative lattice formulation of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges, preserving some supersymmetry and enabling continuum limit without fine tuning.

Contribution

It introduces a mass-deformed lattice construction of 2D N=(4,4) SYM that preserves two supercharges and extends to 4D N=2 SYM via fuzzy sphere configurations.

Findings

Lattice theory preserves two supercharges exactly.

Continuum limit achievable without fine tuning.

Realizes 4D N=2 SYM on fuzzy spheres.

Abstract

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around the minimum of k-coincident fuzzy spheres.