Loop-corrected Entropy of Near-extremal Dilatonic $p$-branes

TL;DR

This paper investigates the entropy-temperature relation of near-extremal dilatonic p-branes, showing that string corrections can restore the ideal-gas behavior even when classical analysis fails due to diverging dilaton.

Contribution

It extends the entropy-temperature relation to dilatonic p-branes with finite horizon dilaton and discusses how string corrections can fix classical breakdowns.

Findings

The ideal-gas relation holds for finite horizon dilaton.

Classical divergence of dilaton indicates breakdown of classical approximation.

String corrections can restore the entropy-temperature relation.

Abstract

It has recently been shown that for certain classical non-dilatonic $p$-branes, the entropy and temperature satisfy the ideal-gas relation $S\sim T^{p}$ in the near-extremal regime. We extend these results to cases where the dilaton is non-vanishing, but nevertheless remains finite on the horizon in the extremal limit, showing that the ideal-gas relation is again satisfied. At the classical level, however, this relation does break down if the dilaton diverges on the horizon. We argue that such a divergence indicates the breakdown of the validity of the classical approximation, and that by taking string and worldsheet loop corrections into account, the validity of the entropy/temperature relation may be extended to include these cases. This opens up the possibility of giving a microscopic interpretation of the entropy for all near-extremal $p$-branes.