Thermodynamics of the localized D2-D6 system

TL;DR

This work constructs an approximate non-extremal extension of Cherkis and Hashimoto’s fully localized D2–D6 solution by a systematic expansion near the D6 core, enabling the study of thermal properties of the dual 3D SU(N_2) gauge theory with N_6 fundamentals. The authors compute the Hawking temperature and horizon area, finding the leading entropy S ~ (8 π^2/27) √(2 N_2^3 N_6) V_2 T_H^2 and showing no first-order corrections in 1/m, consistent with a weak-coupling correspondence point N_2 ~ N_6. They analyze the decoupling limit and dimensional reductions, revealing that the same thermodynamic results hold in 11D and 10D descriptions within their regime of validity, while highlighting breakdowns near the horizon and the limitations of the approximations. The results support a high-temperature, strong-to-weak coupling picture and point to future work on higher-order corrections, horizon-regular completions, and coupling-dependent entropy interpolations relevant to gauge/gravity duality.

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.