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

We study the addition of an irrelevant operator to the = 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 ³) 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.