Entropy of Near-Extremal Black p-branes

TL;DR

This paper surveys the entropy of various p-branes, highlighting cases where the Bekenstein-Hawking entropy aligns with world volume interpretations and confirming entropy calculations with world sheet and statistical methods.

Contribution

It provides a comprehensive analysis of entropy for different p-branes, identifying conditions for simple interpretations and matching near-extremal entropy with world volume theories.

Findings

Non-dilatonic p-branes have a simple world volume entropy interpretation.

Near-extremal entropy of certain branes matches world sheet calculations.

Scaling of entropy with temperature agrees with free field statistical models.

Abstract

We carry out a thorough survey of entropy for a large class of $p$-branes in various dimensions. We find that the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the non-dilatonic $p$-branes, those with the dilaton constant throughout spacetime. The entropy of extremal non-dilatonic $p$-branes is non-vanishing only for the solutions preserving 1/8 of the original supersymmetries. Upon toroidal compactification these reduce to dyonic black holes in 4 and 5 dimensions. For the self-dual string in 6 dimensions, which preserves 1/4 of the original supersymmetries, the near-extremal entropy is found to agree with a world sheet calculation, in support of the existing literature. The remaining 3 interesting cases preserve 1/2 of the original supersymmetries. These are the self-dual 3-brane in 10 dimensions, and the 2- and 5-branes in 11 dimensions. For all of them the scaling of the near-extremal Bekenstein-Hawking entropy with the Hawking temperature is in agreement with a statistical description in terms of free massless fields on the world volume.