A bestiary of black holes on the conifold with fluxes

TL;DR

This paper analyzes black hole solutions in warped deformed conifold backgrounds with fluxes, revealing complex phase transitions related to confinement, deconfinement, and chiral symmetry breaking in the dual cascading gauge theory.

Contribution

It provides a detailed classification of black holes on the conifold with fluxes and explores their phase structure in relation to multiple physical scales.

Findings

Identification of three distinct phase transition patterns.

Recovery of known Klebanov-Tseytlin and Klebanov-Strassler solutions in the decompactification limit.

Elucidation of the interplay between confinement, deconfinement, and chiral symmetry breaking.

Abstract

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.