A double copy for ${\cal N}=2$ supergravity: a linearised tale told on-shell

TL;DR

This work constructs an on-shell, linearised double copy between gauge theories and four-dimensional $N=2$ supergravity coupled to one vector multiplet with quadratic prepotential $F = - i X^0 X^1$, using a position-space convolution framework. A bi-adjoint spectator field is introduced to mediate the double copy and ensure global symmetry invariance, yielding a comprehensive dictionary that maps gravity fluctuations to gauge-theory data. The dictionary is tested in the weak-field limit by mapping dyonic BPS black hole configurations in gravity to purely electric configurations on the gauge theory side, demonstrating consistency with linearised SUSY and equations of motion. The results provide a concrete realisation of gravity-gauge correspondence in a nontrivial supersymmetric setting and lay groundwork for generalisations to more vector multiplets and more intricate backgrounds. The work also highlights the role of algebraic structures like convolutions and spectator fields in realising the double copy beyond simple amplitudes, offering a path toward broader applicability in linearised gravity.

Abstract

We construct the on-shell double copy for linearised four-dimensional ${\cal N}=2$ supergravity coupled to one vector multiplet with a quadratic prepotential. We apply this dictionary to the weak-field approximation of dyonic BPS black holes in this theory.