Entropy of Thermally Excited Black Rings

TL;DR

The paper develops a microscopic description of thermally excited five-dimensional black rings by identifying them with straight black strings and applying a two-dimensional CFT framework with $(4,0)$ supersymmetry. A central result is a Cardy-like entropy formula $S = 2π [ sqrt{ch^{irr}_L/6} + sqrt{ch^{irr}_R/6} ]$ that accounts for all charges, angular momenta, and excitations, and it yields thermodynamic relations via a first-law analysis with left- and right-moving temperatures $T_L$ and $T_R$. Duality analyses reveal the most general black ring in $N=8$ supergravity is characterized by 21 parameters up to duality, with a canonical 9-parameter family extendable to the full set; many of these general thermally excited rings have not yet been constructed in supergravity. The work offers a coherent microscopic picture for non-extremal rings, providing predictions for horizon areas and thermodynamic quantities that can guide future supergravity constructions and deepen the link between black rings, string theory, and dualities.

Abstract

A string theory description of near extremal black rings is proposed. The entropy is computed and the thermodynamic properties are derived for a large family of black rings that have not yet been constructed in supergravity. It is also argued that the most general black ring in N=8 supergravity has 21 parameters up to duality.