Thermodynamics of inhomogeneously mass-deformed ABJM model and pressure anisotropy
Seungjoon Hyun (Department of Physics, Yonsei University, Seoul, 03722, Korea); Byoungjoon Ahn (Department of Physics, Yonsei University, Seoul, 03722, Korea); Kyung Kim (Department of Physics and Astronomy, Sejong University, Seoul, 05006, Korea); O-Kab Kwon (Department of Physics, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 16419, Korea); Sang-A Park (School of Physics, Korea Institute for Advanced Study, Seoul, 02455, Korea, Department of Physics, Yonsei University, Seoul, 03722, Korea)
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.
