Non-Extremality, Chemical Potential and the Infrared limit of Large N Thermal QCD

Non-extremal solution with warped resolved-deformed conifold background is important to study the infrared limit of large N thermal QCD. Earlier works in this direction have not taken into account all the back-reactions on the geometry, namely from the branes, fluxes, and black-hole carefully. In the present work we make some progress in this direction by solving explicitly the supergravity equations of motions in the presence of the backreaction from the black-hole. The backreactions from the branes and the fluxes on the other hand and to the order that we study, are comparatively suppressed. Our analysis reveal, among other things, how the resolution parameter would depend on the horizon radius and how the RG flows of the coupling constants should be understood in these scenarios, including their effects on the background three-form fluxes. We also study the effect of switching on a chemical potential in the background and, in a particularly simplified scenario, compute the actual value of the chemical potential for our case.