Thermodynamics of large N gauge theory from top down holography

By considering fluxes on D7 branes and explicitly computing their back-reaction on the geometry with and without a black hole, we show how the UV divergence of Klebanov-Strassler model can be regulated. Using the form of the metric and fluxes in the extremal and non-extremal limit, we compute the on-shell gravity action including the localized sources up to linear order in perturbation parameter g_sM^2/N, g_sN_f where N,M and N_f are units of D3,D5 and D7 charges in the dual gauge theory. Using the gravitational description, we show how the gauge theory undergoes a first-order Hawking-Page like phase transition and compute the critical temperature T_c. Finally, we obtain the equation of state for the gauge theory by computing thermodynamic state functions of the black hole and exhibit how black holes in deformed cone geometry can lead to results that are qualitatively similar to lattice QCD simulations.