The double copy of maximal supersymmetry in D = 4 - Roberto Bonezzi; Giuseppe Casale; Olaf Hohm (Journal of High Energy Physics)
Abstract We realize off-shell, local and gauge invariant N $$ \mathcal{N} $$ = 8 supergravity in D = 4, to cubic order in fields, as the double copy of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory (SYM). Employing the homotopy algebra approach, we show that, thanks to a redundant formulation for the fermionic fields, the kinematic algebra K $$ \mathcal{K} $$ of N $$ \mathcal{N} $$ = 4 SYM is compatible with an action of the global supersymmetry algebra. The double copy space is then a subspace of K $$ \mathcal{K} $$ ⨂ K ~ $$ \overset{\sim }{\mathcal{K}} $$ that inherits an L ∞ algebra on which the two copies of the N $$ \mathcal{N} $$ = 4 action combine into an action of the N $$ \mathcal{N} $$ = 8 supersymmetry algebra, with a corresponding enhancement of the R-symmetry group to SU(8).