Thermodynamics of the localized D2-D6 system

TL;DR

This paper extends a supergravity solution for D2-D6 branes to include thermal effects, calculating temperature and entropy, and finds the leading order entropy remains unchanged at first order, aligning with weak-coupling predictions.

Contribution

It provides the first non-extremal extension of the localized D2-D6 supergravity solution and analyzes its thermodynamic properties.

Findings

Leading order entropy proportional to N_2^{3/2} N_6^{1/2} T_H^2

First order correction to entropy is zero

Results consistent with weak-coupling predictions at N_2 ~ N_6

Abstract

An exact fully-localized extremal supergravity solution for N_2 D2 branes and N_6 D6 branes, which is dual to 3-dimensional supersymmetric SU(N_2) gauge theory with N_6 fundamentals, was found by Cherkis and Hashimoto. In order to consider the thermal properties of the gauge theory we present the non-extremal extension of this solution to first order in an expansion near the core of the D6 branes. We compute the Hawking temperature and the black brane horizon area/entropy. The leading order entropy, which is proportional to N_2^{3/2} N_6^{1/2} T_H^2, is not corrected to first order in the expansion. This result is consistent with the analogous weak-coupling result at the correspondence point N_2 ~ N_6.