Non-Extremal Gravity Duals for Fractional D3-Branes on the Conifold

The world volume theory on N regular and M fractional D3-branes at the conifold singularity is a non-conformal N = 1 supersymmetric SU(N+ M) SU(N) gauge theory. In previous work the extremal Type IIB supergravity dual of this theory at zero temperature was constructed. Regularity of the solution requires a deformation of the conifold: this is a reflection of the chiral symmetry breaking. To study the non-zero temperature generalizations non-extremal solutions have to beconsidered, andinthehightemperaturephasethechiralsymmetryisexpectedto berestored. SuchasolutionisexpectedtohavearegularSchwarzschild horizon. We construct an ansatz necessary to study such non-extremal solutions and show that thesimplest possiblesolutionhasasingularhorizon. Wederivethesystemofsecond order equations in the radial variable whose solutions may have regular horizons.