On the non-BPS first order flow in $ \mathcal{N} $ = 2 U(1)-gauged Supergravity

Abstract

We consider theories of N = 2 supergravity with Fayet-Iliopoulos gauging and describe a procedure to obtain non-BPS extremal black hole solutions in asymptotically AdS 4 space, in a fully symplectic covariant framework.By considering both electric as well as magnetic gauging, we are able to find new extremal purely magnetic and dyonic solutions. We consistently impose the Dirac quantization condition as a constraint on the black hole and gravitinos charges. This additional requirement allows to parametrize the black hole entropy in terms of an integer and of the entropy of the corresponding black hole in the ungauged model.We also find the nonextremal generalization of the dyonic solution and we compute the product of the areas. For all the configurations with asymptotic supersymmetry we furthermore compute the mass.

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

“…One can break supersymmetry explicitly but preserve extremality by satisfying (2.21) but not (2.16) and indeed the solutions in the literature satisfy the equations of motion when the charges are altered to satisfy (2.21) instead of (2.16) while keeping all metric modes and scalar fields unchanged, a fact which was first noted in [24,25] Throughout this work, while we constantly refer to BPS solutions, everything will apply equally well to solutions which satisfy (2.21) but not (2.16).…”

Black string first order flow in N = 2, d = 5 abelian gauged supergravity

“…e.g. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] for an (incomplete) list of references. In particular, ref.…”

“…Similar to the case of N = 2, d = 4 abelian gauged supergravity [14,17], one introduces a 'field rotation matrix'…”

First order flow for non-extremal AdS black holes and mass from holographic renormalization

“…In analogy with the flat case, also for Anti-de Sitter (AdS) configurations a first order flow has been found for BPS [8][9][10][11] and extremal non-BPS [12,13] black holes in U(1)-gauged supergravity. A superpotential has been found also in this setup, however it does not satisfy any relation of the form (1.2).…”

“…We integrate over a finite time interval, hence the factor β t . It turns out that the explicit form for the part in g 2 is: 13) where the total derivative part is…”