Instantons, black holes and harmonic functions

TL;DR

This paper develops a class of five-dimensional Einstein-Maxwell theories that include vector multiplet Lagrangians, allowing multi-centered black hole solutions and attractor equations, expressed via harmonic functions and related to generalized special geometry.

Contribution

It introduces a new class of five-dimensional theories with supersymmetry-like features, extending the geometric framework beyond traditional special real geometry.

Findings

Solutions expressed through harmonic functions and algebraic equations

Existence of multi-centered black hole solutions

Generalization of very special real geometry

Abstract

We find a class of five-dimensional Einstein-Maxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multi-centered black hole solutions and of attractor equations. Solutions can be expressed in terms of harmonic functions through a set of algebraic equations. The geometry underlying these Lagrangians is characterized by the existence of a Hesse potential and generalizes the very special real geometry of vector multiplets. Our construction proceeds by first obtaining instanton solutions for a class of four-dimensional Euclidean sigma models, which includes those occuring for four-dimensional Euclidean N=2 vector multiplets as a subclass.