Gauge theory description of the fate of the small Schwarzschild blackhole

Abstract

In this talk we discuss the fate of the small Schwarzschild blackhole of $AdS_5\times S^5$ using the AdS/CFT correspondence at finite temperature. The third order $N = \infty$ phase transition in the gauge theory corresponds to the blackhole-string transition. This singularity is resolved using a double scaling limit in the transition region. The phase transition becomes a smooth crossover where multiply wound Polyakov lines condense. In particular the density of states is also smooth at the crossover. We discuss the implications of our results for the singularity of the Lorenztian section of the small Schwarzschild blackhole. (\it {Talk given at the 12th Regional conference in Islamabad, Pakistan, based on hep-th/0605041})