Cosmological constant as confining U(1) charge in two-dimensional dilaton gravity

TL;DR

The paper promotes the cosmological constant to a thermodynamic variable in 2d dilaton gravity by interpreting Λ as a confining U1 charge, requiring a novel Born-Infeld boundary term. It derives a largely model independent thermodynamic framework from Euclidean path integrals, obtaining entropy, enthalpy, volume and a first law that remain valid in the presence of state dependent Λ and multiple U(1) charges. A Schottky anomaly in the specific heat emerges at finite cutoffs, and the formalism is demonstrated in AdS Schwarzschild–Tangherlini, BTZ and Jackiw–Teitelboim models, including charged generalizations and microcanonical considerations. The results connect 2d dilaton gravity thermodynamics to higher dimensional AdS black hole physics and provide a consistent, versatile toolkit for studying confining U1 charges and Λ as a thermodynamic variable.

Abstract

The cosmological constant is treated as a thermodynamical parameter in the framework of two-dimensional dilaton gravity. We find that the cosmological constant behaves as a U(1) charge with a confining potential, and that such potentials require a novel Born-Infeld boundary term in the action. The free energy and other thermodynamical quantities of interest are derived, from first principles, in a way that is essentially model-independent. We discover that there is always a Schottky anomaly in the specific heat and explain its physical origin. Finally, we apply these results to specific examples, like Anti-de Sitter-Schwarzschild-Tangherlini black holes, Banados-Teitelboim-Zanelli black holes and the Jackiw-Teitelboim model.