Duality Invariant Non-Extreme Black Holes in Toroidally Compactified String Theory

TL;DR

This paper develops duality-invariant formulas for thermodynamic properties of non-extreme black holes in toroidally compactified string theories, highlighting invariance under S, T, and U dualities in various dimensions.

Contribution

It provides explicit duality-invariant expressions for non-extreme black hole solutions in five and four dimensions, extending understanding of their thermodynamics in string theory.

Findings

Explicit S- and T-duality invariant formulas in D=5

Leading order duality-invariant expressions in D=4

Framework for analyzing non-extreme solutions in string compactifications

Abstract

We present duality invariant structure of the thermodynamic quantities of non-extreme black hole solutions of torodially compactified Type II (M-theory) and heterotic string in five and four dimensions. These quantities are parameterized by duality invariant combinations of charges and the non-extremality parameter, which measures a deviation from the BPS-saturated limit. In particular, in D=5 we find explicit S- and T-duality [U-duality] invariant expressions for solutions of toroidally compactified heterotic string [Type II string]. In D=4, we consider general S-duality invariant expressions for non-extreme solutions of pure N=4 supergravity and find to the leading order in non-extremality parameter the T- and S-duality invariant expressions of toroidally compactified heterotic string. General non-extreme solutions of toroidally compactified string in D=4 are awaiting further investigation.