Thermodynamics of the N=2* flow

TL;DR

This paper analyzes the thermodynamics of N=2* SU(N) gauge theory at strong coupling using supergravity duals, revealing a positive free energy correction, a temperature-dependent condensate, and thermodynamic inconsistencies.

Contribution

It provides an exact non-extremal supergravity solution for N=2* theory and investigates its thermodynamic properties, highlighting a paradox in the first law of thermodynamics.

Findings

Positive correction to free energy due to mass deformation

Induction of temperature-dependent gaugino condensate

Violation of the first law of thermodynamics in standard analysis

Abstract

We discuss the thermodynamics of the N=2*, SU(N) gauge theory at large 't Hooft coupling. The tool we use is the non-extremal deformation of the supergravity solution of Pilch and Warner (PW) [hep-th/0004063], dual to N=4, SU(N) gauge theory softly broken to N=2. We construct the exact non-extremal solution in five-dimensional gauged supergravity and further uplift it to ten dimensions. Turning to the thermodynamics, we analytically compute the leading correction in m/T to the free energy of the non-extremal D3 branes due to the PW mass deformation, and find that it is positive. We also demonstrate that the mass deformation of the non-extremal D3 brane geometry induces a temperature dependent gaugino condensate. We find that the standard procedure of extracting the N=2* gauge theory thermodynamic quantities from the dual supergravity leads to a violation of the first law of thermodynamics. We speculate on a possible resolution of this paradox.