Peculiar properties of a charged dilatonic black hole in AdS5
Abstract
We study a charged dilatonic black hole in AdS5, derived from a Lagrangian involving a gauge field whose kinetic term is modified by the exponential of a neutral scalar. This black hole has two properties which one might reasonably demand of the dual of a Fermi liquid: Its entropy is proportional to temperature at low temperature, and its extremal limit supports normal modes of massless, charged bulk fermions. The black hole we study has a simple analytic form because it can be embedded in type IIB string theory as the near-horizon limit of D3-branes with equal spins in two of the three independent transverse planes. Two further properties can be deduced from this embedding: There is a thermodynamic instability, reminiscent of ferromagnetism, at low temperatures; and there is an AdS3 factor in the extremal near-horizon geometry which accounts for the linear dependence of entropy on temperature. Altogether, it is plausible that the dilatonic black hole we study, or a relative of it with similar behavior in the infrared, is the dual of a Fermi liquid; however, the particular embedding in string theory that we consider is unlikely to have such a dual description, unless through some unexpected boson-fermion equivalence at large N.
- Publication:
-
Physical Review D
- Pub Date:
- February 2010
- DOI:
- 10.1103/PhysRevD.81.046001
- arXiv:
- arXiv:0911.2898
- Bibcode:
- 2010PhRvD..81d6001G
- Keywords:
-
- 11.25.Tq;
- 04.70.-s;
- 11.10.Wx;
- Gauge/string duality;
- Physics of black holes;
- Finite-temperature field theory;
- High Energy Physics - Theory
- E-Print:
- 27 pages, 1 figure. v2: Some references added