On the Uniqueness of Supersymmetric Attractors

TL;DR

This paper proves the uniqueness of supersymmetric attractors in four-dimensional N=2 supergravity theories with specific charge configurations, including axionic cases, and provides explicit conditions for this uniqueness.

Contribution

It establishes the conditions under which supersymmetric attractors are unique, extending the analysis to axionic cases and exemplifying with a two-parameter model.

Findings

Axion-free attractors are unique for given charges.

Explicit conditions for the uniqueness of axionic attractors.

Complete solutions for a two-parameter model's attractor equations.

Abstract

In this paper we discuss the uniqueness of supersymmetric attractors in four dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness.