A topological perspective on bulk boundary thermodynamic equivalence

TL;DR

This paper reveals a precise duality between the thermodynamics of five-dimensional charged Gauss-Bonnet AdS black holes and the boundary conformal field theory, linking bulk topological charges with boundary phase transition characteristics.

Contribution

It establishes an exact duality connecting bulk black hole thermodynamics with boundary CFT thermodynamics, including topological and phase transition aspects.

Findings

Exact duality between bulk and boundary thermodynamics.

Topological charges match between bulk black holes and boundary CFT.

Correspondence of extended first laws in bulk and boundary theories.

Abstract

We establish an exact duality between the extended thermodynamics of five-dimensional charged Gauss-Bonnet AdS black holes and the thermodynamic framework of the dual boundary conformal field theory (CFT). The thermodynamics of the dual CFT involves two central charges originating from the trace anomaly. We demonstrate a precise correspondence between the extended first laws on the bulk and boundary sides. Moreover, the topological charges of the CFT thermodynamics, associated with the phase transition and critical point, coincide with those of the corresponding bulk black hole.