d=4 Attractors, Effective Horizon Radius and Fake Supergravity

TL;DR

This paper studies extremal black hole attractors in N=3 and N=5 supergravity in four dimensions, exploring their properties, similarities to other theories, and the role of fake supergravity formalism.

Contribution

It provides a detailed analysis of attractor solutions in N=3 and N=5 supergravity, highlighting their relation to N=2 and N=4 theories and discussing the absence of five-dimensional uplift.

Findings

Attractors in N=3 are similar to N=2 minimally coupled supergravity.

N=5 attractors resemble N=4 pure supergravity attractors.

Only 1/4-BPS non-degenerate solutions exist in N=5 theories.

Abstract

We consider extremal black hole attractors (both BPS and non-BPS) for N=3 and N=5 supergravity in d=4 space-time dimensions. Attractors for matter-coupled N=3 theory are similar to attractors in N=2 supergravity minimally coupled to Abelian vector multiplets. On the other hand, N=5 attractors are similar to attractors in N=4 pure supergravity, and in such theories only 1\N-BPS non-degenerate solutions exist. All the above mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a d=5 uplift. Finally we comment on the "duality" relations among the attractor solutions of N\geq2 supergravities sharing the same full bosonic sector.