Large and small non-extremal black holes, thermodynamic dualities, and the Swampland
Niccolò Cribiori, Markus Dierigl, Alessandra Gnecchi, Dieter Lüst, Marco Scalisi
Abstract
A bstract In this paper we discuss black hole solutions parametrized by their entropy $$ \mathcal{S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> and temperature $$ \mathcal{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> in gravitational effective theories. We are especially interested in the analysis of the boundary regions in the $$ \mathcal{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> − $$ \mathcal{S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> 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 entropy- or temperature-distance . The effective theories with scalars we investigate are Einstein-Maxwell-dilaton theory as well as $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 supergravity black holes, these 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.