Multi-centered ${\mathcal N}=2$ BPS black holes: a double copy description

TL;DR

This work develops an on-shell double copy dictionary for linearised $\mathcal{N}=2$ supergravity coupled to $n_V$ vector multiplets and applies it to construct a double copy description of multi-centered dyonic BPS black holes in the weak-field limit. The construction uses a convolution-based dictionary with a spectator bi-adjoint field to map gravitational fluctuations to products of a rigid $\mathcal{N}=2$ SYM theory and a bosonic YM sector, ensuring consistency with linearised SUSY and special geometry constraints. For multi-centered solutions, the authors derive explicit expressions such as $X^I = \Sigma^I/r$ and show that the metric perturbation is reproduced from $A_\mu \star \tilde{A}_\nu$, connecting charges and moduli to the gauge-theory data. The results hint at potential holographic-like interpretations for flat-space gravity and motivate further study of asymptotic symmetries within the double copy framework.

Abstract

We present the on-shell double copy dictionary for linearised ${\mathcal N}=2$ supergravity coupled to an arbitrary number of vector multiplets in four dimensions. Subsequently, we use it to construct a double copy description of multi-centered BPS black hole solutions in these theories in the weak-field approximation.