We study dual geometries to a deformed ABJM model with spatially dependent source functions at finite temperature. These source functions are proportional to the mass function m(x) = m 0 sin kx and its derivative m (x). As dual geometries, we find hairy black branes and AdS solitons corresponding to deconfinement phase and confining phase of the dual field theory, respectively. It turns out that the hairy AdS solitons has lower free energy than the black branes when the Hawking temperature is smaller than the confining scale. Therefore the dual system undergoes the first order phase transition. Even though our study is limited to the so-called Q-lattice ansatz, the solution space contains a set of solutions dual to a supersymmetric mass deformation. As a physical quantity to probe the confining phase, we investigate the holographic entanglement entropy and discuss its behavior in terms of modulation effect.
By using the scaling symmetry in the reduced action formalism, we derive the novel Smarr relation which holds even for the hairy rotating AdS 3 black holes. And then, by using the Smarr relation we argue that the hairy rotating AdS 3 black holes are stable thermodynamically, compared to the non-hairy ones. *
By considering the behavior of the reduced action under the scaling transformation, we present a unified derivation of the Smarr-like relation for asymptotically anti-de-Sitter planar black holes.This novel Smarr-like relation leads to useful information in the condensed matter systems through the AdS/CMT correspondence. By using our results, we provide an efficient way to obtain the holographically renormalized on-shell action without the information on the explicit forms of counter terms. We find the complete consistency of our results with those in various models discussed in the recent literatures and obtain new implications. *
In this paper we study the thermodynamics of black branes with a modulated complex scalar in the context of bulk and boundary theories. The modulation induces inhomogeneity to the dual field theory, anisotropic pressure, and brane charge to the bulk geometry. The first law of thermodynamics and the Smarr relation are obtained using the off-shell ADT and the reduced action formalisms. We discuss the prescription for the mass of black branes, which relies on relevant and marginal deformations in the dual field theory. One of the cases is the gravity dual to a ABJM model with a sinusoidal mass function depending on a spatial coordinate. This is the first study of the deformed ABJM model at finite temperature including bulk thermodynamics.
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