Maximal super Yang-Mills theories on curved background with off-shell supercharges

TL;DR

This paper develops maximally supersymmetric Yang-Mills theories on curved spaces with off-shell supercharges, expanding the types of backgrounds where supersymmetry can be preserved and providing explicit examples including a reduction from N=4 super Yang-Mills.

Contribution

It generalizes off-shell supersymmetry constructions to curved backgrounds in d<=7 dimensions, extending previous on-shell frameworks and providing explicit models.

Findings

Constructed supersymmetric theories on various curved backgrounds.

Identified preserved supersymmetries for different geometries.

Reduced N=4 super Yang-Mills on RxS^3 to a maximally supersymmetric theory.

Abstract

We construct d<=7 dimensional maximally supersymmetric Yang-Mills theories on a class of curved backgrounds with off-shell supercharges. The off-shell supersymmetry is mainly a generalization of on-shell supersymmetry constructed previously by Blau. We present several examples of backgrounds and discuss the number of the preserved supersymmetries on these backgrounds. We also construct another maximally supersymmetric Yang-Mills theories on S^3 by dimensional reducing along the R-direction of N=4 super Yang-Mills theory on RxS^3.