Duality invariance in Fayet-Iliopoulos gauged supergravity

Abstract

We propose a geometric method to study the residual symmetries in N = 2, d = 4 U(1) Fayet-Iliopoulos (FI) gauged supergravity. It essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. In particular we are interested in those transformations that act non-trivially on the solutions and produce scalar hair and dyonic black holes from a given seed. We illustrate the procedure for finding this group in general and then show how it works in some specific models. For the prepotential F = −iX 0 X 1 , we use our method to add one more parameter to the rotating Chow-Compère solution, representing scalar hair.

AdS5 black strings in the stu model of FI-gauged N = 2 supergravity

“…with L = G, V ≡ G t ΩV, where V denotes the covariantly holomorphic symplectic section, G = (g Λ , g Λ ) t is the symplectic vector of FI parameters and D the Kählercovariant derivative. More details can be found e. g. in [2,[23][24][25].…”

“…Recently however, elaborating on earlier work [9], the authors of [2] developed a solution generating technique for N = 2, d = 4 Fayet-Iliopoulos (FI)-gauged supergravity as well, which essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. One of the main goals of the present paper is to provide an explicit application of the method introduced in [2]. Namely, we start from the supersymmetric domain wall black hole in the stu model of N = 2, d = 4 FI-gauged supergravity, with prepotential F = −X 1 X 2 X 3 /X 0 , constructed in [1].…”

“…Namely, we start from the supersymmetric domain wall black hole in the stu model of N = 2, d = 4 FI-gauged supergravity, with prepotential F = −X 1 X 2 X 3 /X 0 , constructed in [1]. We then act on it with one of the symmetry transformations of [2] and lift the resulting configuration to five dimensions. This leads to a dyonic black string in minimal N = 2, d = 5 gauged supergravity, with momentum along the string 2 .…”

“…The remainder of this paper is organized as follows: In the next section, we briefly introduce the stu model of N = 2, d = 5 FI-gauged supergravity and the r-map which relates it to the corresponding four-dimensional model. We also determine the residual duality symmetries of the latter along the recipe of [2], and review the domain wall black hole seed solution constructed in [1]. In section 3, this configuration is lifted to d = 5, and it is shown that the result is a black string with momentum along the string.…”

On the on-shell: the action of AdS4 black holes

“…This includes the class of black holes in [3,21] as well as those related by duality transformation [28,39].…”