Bulk-boundary thermodynamic equivalence: a topology viewpoint

• Published in: The journal of high energy physics Vol. 2023; no. 6; pp. 115 - 17
• Main Authors: Zhang, Ming, Jiang, Jie
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 20.06.2023; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Classical and Quantum Gravitation; Classical Theories of Gravity; Cosmological constant; Elementary Particles; Energy; Equivalence; Field theory; Gravity; High energy physics; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spacetime; String Theory; Thermodynamics; Topology; Classical Theories of Gravity; AdS-CFT Correspondence; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2023)115

A bstract Setting the cosmological constant to be dynamical, we study the bulk and boundary thermodynamics of charged Anti-de Sitter black holes. We develop mass/energy formulas in terms of thermodynamic state functions for the extended thermodynamics, mixed thermodynamics, and boundary conformal field theory thermodynamics. We employ the residue method to study the topological properties of the phase transitions. Our analysis reveals that the bulk and boundary thermodynamics are topologically equivalent for both criticalities and first-order phase transitions in the canonical ensembles, as well as for the Hawking-Page(-like) phase transitions in the grand canonical ensembles. Additionally, those three kinds of phase transitions are shown to be distinguished by their unique topological charges. Our results exemplify the gravity-gauge duality in terms of topology.