Holography of charged dilaton black holes

Abstract

We study charged dilaton black branes in AdS 4 . Our system involves a dilaton φ coupled to a Maxwell field F µν with dilaton-dependent gauge coupling, 1 g 2 = f 2 (φ). First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where f (φ) = e αφ , are Lifshitz-like, with a dynamical exponent z determined by α. The black hole thermodynamics varies in an interesting way with α, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like ω 2 at T = 0 independent of α. We also explore the charged black brane physics of several other classes of gauge-coupling functions f (φ). In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from AdS 2 × R 2 .

Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole

“…First, besides going beyond the massless case and heating up the dual soup to the finite temperature, it is interesting to investigate the probe fermion in other desirable dilatonic black holes such as those obtained in [22,23], where the near horizon geometry has a favorable Lifshitz symmetry. In addition, as done in [24,25,26,27,28], one is also tempted to investigate how the fermionic correlator is modified in the presence of the bulk dipole coupling.…”

Transport properties of spacetime-filling branes

“…The effective action (1.7) is the Legendre-tranformed version of an Einstein-Maxwell-Dilaton (EMD) system, where only the time-component of the gauge potential is turned on, and expressed in terms of the conjugate variable ρ. This type of systems were studied in detail in [14,24,25]. For a non trivial potential there exist solutions with hyperscaling-violating metric and Lifshitz scaling, as well as a log-behaved dilaton.…”

“…The specific heat at fixed charge is obtained straightforwardly 24) where the final result is written in terms of r + , ̺ and T to give a more compact expression and show explicitly the non-negativeness. At fixed chemical potential the specific heat is also non-negative definite, C µ ≥ 0.…”

On attractor mechanism ofAdS4black holes

“…A careful analysis of charged dilaton black holes in AdS 4 was initiated in [2]. The focus of that work was on extremal and near-extremal solutions when the scalar potential is constant (proportional to the cosmological constant).…”

“…That is, these solutions can exhibit new features which are absent for theories with a trivial dilaton potential [2]. For example, the extremal limit black hole solutions can have a finite horizon area even if just one electric field is turned on.…”