A Deep Dive into classical and Topological CFT Thermodynamics in Lifshitz and Hyperscaling Violating Black Holes

TL;DR

This paper explores the thermodynamics and phase transitions of Lifshitz and hyperscaling violating black holes using classical and topological methods within the holographic framework, enhancing understanding of their CFT duals.

Contribution

It develops a comparative analysis of classical and topological approaches to black hole thermodynamics in Lifshitz and HSV models, demonstrating their equivalence and providing new insights into phase behavior.

Findings

Classical and topological methods yield consistent phase transition results.

Topological approach offers a more accessible alternative to classical analysis.

Enhanced understanding of black hole thermodynamics in Lifshitz and HSV contexts.

Abstract

To effectively utilize the AdS/CFT correspondence, a precise set of rules must be established to guide the translation of computed quantities in the gravitational sector into their CFT counterparts, and vice versa. This framework is commonly referred to as the holographic dictionary. The formulation of such dictionaries opens a two-way gateway, allowing researchers to extend theoretical principles and findings from one domain into the other for further exploration and study. The development of a holographic dictionary for Lifshitz black holes and hyperscaling violation (HSV) models \cite{6} has provided an essential foundation for studying CFT thermodynamics and phase behavior of these black holes. Based on this framework, we will investigate their thermodynamic properties using two distinct approaches. In the first step, we adopt the classical and traditional method, identifying critical points to examine the behavior of the free energy function as a function of temperature near the critical boundary. By analyzing its behavior, we will study phase transitions and then proceed to evaluate the stability of the models. In the next step, to compare both methodologies and highlight their equivalence, particularly demonstrating the accessibility of the topological method compared to the classical approach, we will analyze phase behavior through the lens of topological charges.