Clearing the Throat: Irrelevant Operators and Finite Temperature in Large N Gauge Theory

We study the addition of an irrelevant operator to the N = 4 supersymmetric large N SU(N) gauge theory, in the presence of finite temperature, T . In the supergravity dual, the effect of the operator is known to correspond to a deformation of the AdS5 × S5 “throat” which restores the asymptotic ten dimensional Minkowski region of spacetime, completing the full D3–brane solution. The system at non–zero T is interesting, since at the extremes of some of the geometrical parameters the geometry interpolates between a seven dimensional spherical Minkowskian Schwarzschild black hole (times R3) and a five dimensional flat AdS Schwarzschild black hole (times S5). We observe that when the coupling of the operator reaches a critical value, the deconfined phase, which is represented by the geometry with horizon, disappears for all temperatures, returning the system to a confined phase which is represented by the thermalised extremal geometry.