Non-Abelian, supersymmetric black holes and strings in 5 dimensions

TL;DR

This paper constructs and analyzes the first supersymmetric non-Abelian black-hole and black-string solutions in five-dimensional supergravity, revealing new insights into their gauge fields, entropies, and relations to four-dimensional theories.

Contribution

It introduces novel supersymmetric solutions with non-trivial SU(2) gauge fields in 5D supergravity, extending previous classifications and connecting 5D and 4D solutions through dimensional reduction.

Findings

Black holes and strings with non-Abelian gauge fields are constructed.

Instantons and monopoles influence entropy but not mass or tension.

The solution construction connects 5D and 4D supersymmetric solutions.

Abstract

We construct and study the first supersymmetric black-hole and black-string solutions of non-Abelian-gauged N=1,d=5 supergravity (N=1,d=5 Super-Einstein-Yang-Mills theory) with non-trivial SU(2) gauge fields: BPST instantons for black holes and BPS monopoles of different kinds ('t~Hooft-Polyakov, Wu-Yang and Protogenov) for black strings and also for certain black holes that are well defined solutions only for very specific values of all the moduli. Instantons, as well as colored monopoles do not contribute to the masses and tensions but do contribute to the entropies. The construction is based on the characterization of the supersymmetric solutions of gauged N=1,d=5 supergravity coupled to vector multiplets achieved in Ref. Bellorin:2007yp which we elaborate upon by finding the rules to construct supersymmetric solutions with one additional isometry, both for the timelike and null classes. These rules automatically connect the timelike and null non-Abelian supersymmetric solutions of N=1,d=5 SEYM theory with the timelike ones of N=2,d=4 SEYM theory by dimensional reduction and oxidation. In the timelike-to-timelike case the singular Kronheimer reduction recently studied in Ref. Bueno:2015wva plays a crucial role.