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

Abstract

Abstract: We construct and study the first supersymmetric black-hole and black-string solutions of non-Abelian-gauged (Formula presented.) , d = 5 supergravity ((Formula presented.) , 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 (Formula presented.) , d = 5 supergravity coupled to vector multiplets achieved in ref. [1] 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 (Formula presented.) , d = 5 SEYM theory with the timelike ones of (Formula presented.) , d = 4 SEYM theory [2, 3] by dimensional reduction and oxidation. In the timelike-to-timelike case the singular Kronheimer reduction recently studied in ref. [4] plays a crucial role.