Stationary solutions of N=2 supergravity

TL;DR

<3-5 sentence high-level summary> This paper develops a general framework for stationary solutions in four-dimensional $N=2$ supergravity with vector multiplets by exploiting special geometry. It shows that unbroken supersymmetry constrains the holomorphic symplectic section and that the full bosonic configuration is determined by a set of harmonic functions, yielding a Tod's IWP-type metric and explicit relations for the warp factor $e^{-2U}$ and the Kähler connection $Q_m$. The authors illustrate the method with explicit examples, including rotating black holes, Taub–NUT and Eguchi–Hanson instantons in the STU model, and static limits with worldsheet instanton corrections near vanishing Calabi–Yau cycles. This approach unifies known black-hole solutions within $N=2$ supergravity, while also accommodating quantum corrections and potential Calabi–Yau moduli-space phase transitions, offering a versatile tool for exploring singularities and their physical implications.

Abstract

We discuss general bosonic stationary configurations of N=2, D=4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special Kähler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson like instantons for the STU model. In addition, we discuss, in the static limit, worldsheet instanton corrections to the STU black hole solution, in the neighbourhood of a vanishing 4-cycle of the Calabi-Yau manifold. Our procedure is quite general and includes all known black hole solutions that can be embedded into N=2 supergravity.