The Double Copy of Maximal Supersymmetry in $D=10$

TL;DR

This paper uses homotopy algebra techniques to derive double copy relations between ten-dimensional super-Yang-Mills theory and supergravity, revealing how maximal supersymmetry emerges from gauge theories.

Contribution

It extends the homotopy algebra framework to ten-dimensional super-Yang-Mills, deriving supergravity double copies and elucidating supersymmetry structures.

Findings

Derived double copy relations to cubic order in fields.

Showed super-Lie algebra of supersymmetries doubles to maximal supergravity.

Connected gauge theory supersymmetries with supergravity supersymmetries.

Abstract

We continue the program of using homotopy algebras to obtain off-shell, local and gauge redundant derivations of the double copy relations between gauge theory and gravity. We apply it to $N=1$ super-Yang-Mills theory in $D=10$ in order to obtain type IIA or type IIB supergravity, at least to cubic order in fields. Furthermore, we show how the super-Lie algebra of global supersymmetries, acting on the homotopy algebra of $N=1$ super-Yang-Mills theory, double copies to the maximal supersymmetry of supergravity.