Large and Small Non-extremal Black Holes, Thermodynamic Dualities, and the Swampland

TL;DR

This paper explores the thermodynamic properties of black holes in various theories, linking their entropy and temperature limits to Swampland constraints and dualities, revealing deep connections between black hole physics, scalar fields, and string theory.

Contribution

It establishes a connection between black hole thermodynamics and Swampland conjectures, introducing thermodynamic dualities related to string dualities in supergravity and string compactifications.

Findings

Scalar field excursions relate to entropy and temperature distances.

Thermodynamic dualities correspond to T- and S-dualities in supergravity.

Limits of black hole parameters connect to light tower of states in string theory.

Abstract

In this paper we discuss black hole solutions parametrized by their entropy $\mathcal{S}$ and temperature $\mathcal{T}$ in gravitational effective theories. We are especially interested in the analysis of the boundary regions in the $\mathcal{T}-\mathcal{S}$ diagram, i.e. large/small values of entropy and temperature, and their relation to Swampland constraints. To explore this correlation, we couple the gravitational theories to scalar fields and connect limits of thermodynamic quantities of black holes to scalar field excursions in the corresponding solutions. Whenever the scalar fields traverse an infinite field distance, the Swampland Distance Conjecture allows for a reformulation in terms of {\it entropy-} or {\it temperature-distance}. The effective theories with scalars we investigate are Einstein-Maxwell-dilaton theory as well as $\mathcal{N} = 2$ supergravity in four dimensions. The relation of the latter to type II string theory compactified on Calabi-Yau 3-folds often allows for a direct identification of the corresponding light tower of states. These setups also point towards various dualities between asymptotic regions of the black hole solution. In the context of $\mathcal{N} = 2$ supergravity black holes, these {\it thermodynamic dualities} have an interpretation in terms of T- and S-dualities along the internal directions and their natural action on Kaluza-Klein and winding states.