Abstract
We present a family of exact planar hairy neutral black hole solutions in extended supergravity with Fayet-Iliopoulos (FI) terms. We consider a model where the magnetic part of FI sector vanishes and obtain the superpotential at finite temperature in analytic form. Then, we discuss the thermodynamics and some holographic properties of these solutions. We regularize the action by two different methods, one with gravitational and scalar counterterms and the other using the thermal superpotential as a counterterm, and compute the holographic stress tensor. We also construct the c-function of the corresponding RG flow and obtain an exact holographic β-function for this model.
Highlights
Couplings, combined with the fact that the motion in the radial direction is related to scaling in the dual field theory
These studies suggest that conditions for the existence of hairy black hole solutions comprise suitable scalar field selfinteraction properties, encoded in a scalar potential, together with an appropriate gravitational interaction determining the near-horizon behaviour as well as the far-region hair physics
We have described a supergravity framework and obtained exact neutral planar hairy black holes that, within AdS-CFT duality, can generate non-trivial RG flows in the dual field theory
Summary
The construction of stationary black hole configurations is motivated by the study of classical general relativity solutions as well as AdS-CFT duality. The only known mechanism for introducing a non-trivial scalar potential without explicitly breaking supersymmetry is the so-called gauging procedure [35,36,37,38] The latter can be seen as a deformation of an ungauged theory, with the same amount of supersymmetry and field content, where a suitable subgroup of the global symmetry group of the Lagrangian is promoted to local symmetry, to be gauged by the vector fields. If the special Kähler isometries are not involved in the gauging, the constraints imply that only a U(1) subgroup of SU(2) can be gauged In this case, the embedding tensor has only one non-vanishing component and the resulting theory is deformed by the introduction of abelian electric-magnetic FI terms defined by a constant symplectic vector θM , which encodes all the gauge parameters.. This kind of models can feature unexpected symmetries involving parameter transformations with non-trivial action, providing a new solution generating technique in asymptotically AdS spacetimes5 [10]
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