BPS Solutions of 4d Euclidean N=2 Supergravity with Higher Derivative Interactions

TL;DR

This paper analyzes BPS solutions in four-dimensional Euclidean N=2 supergravity with higher-derivative interactions, deriving attractor and stabilization equations, and providing a framework for studying supersymmetric saddles without analytic continuation.

Contribution

It extends the analysis of BPS solutions to Euclidean signature with higher-derivative terms, deriving new attractor and stabilization equations in this setting.

Findings

Derived Euclidean attractor equations for BPS black holes.

Extended stabilization equations to Euclidean signature.

Provided a framework for supersymmetric saddle analysis without analytic continuation.

Abstract

We study fully BPS and a broad class of half-BPS stationary configurations of four-dimensional Euclidean N=2 supergravity with higher-derivative interactions. Working within the off-shell conformal supergravity framework of de Wit and Reys (arXiv:1706.04973), we analyse the complete set of Killing spinor equations and obtain the corresponding algebraic and differential constraints. We further derive the Euclidean attractor equations and evaluate the Wald entropy for the fully BPS AdS_2 x S^2 background. For half-BPS stationary configurations, we obtain the generalized stabilization equations expressing all fields in terms of harmonic functions on three-dimensional flat base space, extending the Lorentzian analysis of Cardoso et al (arXiv:hep-th/0009234) to the Euclidean signature. Our results provide a framework for studying supersymmetric saddles and computing the gravitational indices entirely within Euclidean higher-derivative supergravity, without recourse to analytic continuation.