Twisted supersymmetries in lattice ${\cal N}=4$ super Yang-Mills theory

TL;DR

This paper investigates the restoration of full supersymmetry in a lattice formulation of ${\cal N}=4$ super Yang-Mills theory, showing that symmetry restoration likely occurs automatically in the continuum limit without additional fine-tuning.

Contribution

The authors derive the form of the remaining twisted supersymmetries by combining discrete R-symmetries with scalar supersymmetry, suggesting automatic enhancement to full supersymmetry in the continuum limit.

Findings

Remaining supersymmetries are likely restored in the continuum limit.

Restoration of rotational symmetry implies R-symmetry restoration.

Full ${\cal N}=4$ supersymmetry may emerge without fine-tuning.

Abstract

Recently it has been shown how a topologically twisted version of ${\cal N}=4$ super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The remaining fifteen supersymmetries are broken by terms of ${\cal O}(a)$ where $a$ is the lattice spacing. One would like to know whether these remaining supersymmetries are regained in the continuum limit $a \to 0$ and, if not, how much tuning of the couplings in the lattice action is required. In this paper we derive the form of these additional twisted supersymmetries by combining a set of discrete R-symmetries of the continuum theory with the action of the scalar supersymmetry. We then argue that restoration of rotational symmetry in the continuum limit of the lattice theory likely implies restoration of R-symmetry and hence should lead to an automatic enhancement to the full ${\cal N}=4$ supersymmetry without further fine-tuning.