Massless spin-two field S-duality

TL;DR

This paper reviews homological algebra tools in de Rham theory and explores the potential extension of S-duality symmetry to non-Abelian gauge theories like Yang-Mills and Einstein, suggesting it may be non-perturbative.

Contribution

It provides a review of algebraic tools for higher spin gauge structures and discusses theoretical prospects for non-Abelian S-duality extensions beyond local perturbative frameworks.

Findings

Homological algebra tools are essential for understanding higher spin gauge structures.

M-theory suggests possible non-Abelian S-duality extensions.

No-go theorems indicate such extensions may be non-perturbative and outside local field theory scope.

Abstract

We present a review of the homological algebra tools involved in the standard de Rham theory and their subsequent generalizations relevant for the understanding of free massless higher spin gauge structure. M-theory arguments suggest the existence of an extension of (Abelian) S-duality symmetry for non-Abelian gauge theories, like the four dimensional Yang-Mills or Einstein theories. Some no-go theorems prove that this extension, if it exists, should fall outside the scope of local perturbative field theory.