A bestiary of black holes on the conifold with fluxes

We present a comprehensive analysis of the black holes on warped deformed conifold with fluxes in Type IIB supergravity. These black holes realize the holographic dual to thermal states of the ${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of Klebanov et.al on round $S^3$. There are three distinct mass scales in the theory: the strong coupling scale $\Lambda$ of the cascading gauge theory, the compactification scale $\mu=1/L_3$ (related to the $S^3$ radius $L_3$) and the temperature $T$ of a thermal state. Depending on $\Lambda\,,\, \mu$ and $T$, there is an intricate pattern of confinement/deconfinement (Hawking-Page) and the chiral symmetry breaking phase transitions. In the $S^3\to {\mathbb R}^3$ decompactification limit, $i.e$, $\mu\to 0$, we recover the Klebanov-Tseytlin and the Klebanov-Strassler black branes.