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.
Highlights
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. [1] which we elaborate upon by finding the rules to construct supersymmetric solutions with one additional isometry, both for the timelike and null classes
In order to apply these techniques to the case of theories of gravity coupled to fundamental matter fields we must embed the theories first in supergravity theories. d = 4 EYM theories can be embedded almost trivially in N = 1, d = 4 gauged supergravity coupled to vector supermultiplets, but there are no supersymmetric black-hole or more general particle-like solutions in N = 1, d = 4 supergravity: all the supersymmetric solutions of these theories belong to the null class2 and describe, generically, massless solutions such as gravitational waves and black strings
This paper is organized as follows: in section 2 we review the gauging of a nonAbelian group of isometries of an N = 1, d = 5 supergravity theory coupled to vector multiplets
Summary
(the expression that follows from the general formula in ref. [20]) vanishes identically for the kind of gaugings considered here, owing to the property eq (2.12). This fact is associated to the vanishing of the corresponding fermion shift in the gauginos’ supersymmetry transformations
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