Off-Shell Formulation of Simple Supersymmetric Yang-Mills

TL;DR

This paper develops an off-shell formulation for simple supersymmetric Yang-Mills theories in 6 and 10 dimensions, utilizing algebraic structures like quaternions, pure spinors, and soft Lie algebras to ensure algebra closure.

Contribution

It introduces a novel off-shell formulation for higher-dimensional supersymmetric Yang-Mills theories, incorporating auxiliary fields and algebraic tools for superspace construction.

Findings

Off-shell formulation achieved for 6D and 10D supersymmetric Yang-Mills.

Use of pure spinors and soft Lie algebra to close the supersymmetry algebra.

Connections established with earlier foundational works by Evans and Berkovits.

Abstract

An off-shell formulation for 6 and 10 dimensions simple supersymmetric Yang-Mills theories is presented. While the fermionic fields couple to left action of S^3 and S^7 respectively, the auxiliary ones couple to right action (and vice versa). To close the algebra off-shell, left and right actions must commute. For 6 dimensions quaternions work fine. The 10 dimensional case needs special care. Pure spinors and soft Lie algebra (algebra with structure functions instead of structure constants) are essential. Some tools useful for constructing the superspace are also derived. We show how to relate our results to the early works of Evans and Berkovits.