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

TL;DR

The paper develops a complete Euclidean, higher-derivative $ ext{N}=2$ supergravity framework (via off-shell conformal supergravity) to analyze fully BPS and broad half-BPS stationary configurations. It derives the Killing spinor constraints, Euclidean attractor equations, and Wald entropy for the fully BPS AdS$_2\times$S$^2$ background, and formulates generalized stabilization equations expressing half-BPS fields in terms of harmonic functions on a flat 3d base. The results provide a self-contained Euclidean description of supersymmetric saddles and gravitational indices, enabling localization-inspired analyses without analytic continuation. This work lays the groundwork for a deeper understanding of Euclidean attractor mechanisms and the intrinsic counting of microstates in Euclidean higher-derivative supergravity.

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.