Brane-anti-brane Democracy

TL;DR

This paper proposes a duality-invariant formula for black hole entropy and temperature in supersymmetric string theory, unifying extremal and non-extremal solutions through SU(8) covariant charges and brane-antibrane interpretations.

Contribution

It introduces a duality-invariant entropy formula involving 56 SU(8) covariant charges and a second auxiliary 56, enabling classification of black holes across different supersymmetry states.

Findings

Provides a unified entropy formula interpolating between Schwarzschild and extremal black holes.

Uses duality and symmetry considerations to explain the simplicity of the black hole area formula.

Relates brane and anti-brane numbers to fundamental representations of E(7).

Abstract

We suggest a duality invariant formula for the entropy and temperature of non-extreme black holes in supersymmetric string theory. The entropy is given in terms of the duality invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymmetries and therefore serves for classification of black holes in supersymmetric string theories. We introduce the second auxiliary 56 via E(7) symmetric constraint. The symmetric and antisymmetric combinations of these two multiplets are related via moduli to the corresponding two fundamental representations of E(7): brane and anti-brane "numbers." Using the CPT as well as C symmetry of the entropy formula and duality one can explain the mysterious simplicity of the non-extreme black hole area formula in terms of branes and anti-branes.