Supersymmetric Yang-Mills Equations in 10+2 Dimensions

TL;DR

This paper develops a supersymmetric Yang-Mills model in 10+2 dimensions using a null vector, demonstrating its invariance, reduction to known theories, and superspace formulation, thus extending the understanding of higher-dimensional supersymmetric gauge theories.

Contribution

It introduces a consistent supersymmetric Yang-Mills model in 10+2 dimensions with novel invariance properties and reduction mechanisms, including a superspace formulation.

Findings

Reduces to standard 10D supersymmetric Yang-Mills upon dimensional reduction.

Provides a superspace formulation for the 10+2 dimensional model.

Establishes invariance under generalized translations and gauge transformations.

Abstract

We present a model for supersymmetric Yang-Mills theory in 10+2 dimensions. Our construction uses a constant null vector, and leads to a consistent set of field equations and constraints. The model is invariant under generalized translations and an extra gauge transformation. Ordinary dimensional reduction to ten dimensions yields the usual supersymmetric Yang-Mills equations, while dimensional reduction to 2+2 yields supersymmetric Yang-Mills equations in which the Poincar\'e supersymmetry is reduced by a null vector. We also give the corresponding formulation in superspace.