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 mathcal{N} = 1 supersymmetric SU(N) × SU(N + M) cascading gauge theory of Klebanov et al. [1, 2] on round S3. There are three distinct mass scales in the theory: the strong coupling scale Λ of the cascading gauge theory, the compactification scale μ = 1/L3 (related to the S3 radius L3) and the temperature T of a thermal state. Depending on Λ, μ and T, there is an intricate pattern of confinement/deconfinement (Hawking-Page) and the chiral symmetry breaking phase transitions. In the S3 → ℝ3 decompactification limit, i.e., μ → 0, we recover the Klebanov-Tseytlin [3] and the Klebanov-Strassler [4] black branes.
Highlights
An exciting aspect of the gauge theory/string theory correspondence [5, 6] is that it geometrizes the confinement/deconfinement transitions of strongly coupled gauge theories as topology changing transitions in dual supergravity backgrounds
We present a comprehensive analysis of the black holes on warped deformed conifold with fluxes in Type IIB supergravity
The access to the numerical data for the chiral symmetry breaking for the black branes on the conifold [11] greatly simplifies our task: using the map (6.27), with (6.30) and (6.31), we identify from the data in [11] the onset of the chiral symmetry breaking at μ = 0 to occur at
Summary
An exciting aspect of the gauge theory/string theory correspondence [5, 6] is that it geometrizes the confinement/deconfinement transitions of strongly coupled gauge theories as topology changing transitions in dual supergravity backgrounds. Tcbon,A — confined thermal states with the boundary S3 smoothly shrinking to zero size (the top row, right panel) In these states the chiral symmetry of the gauge theory is spontaneously broken. Tdsecon — deconfined thermal states with the Euclidean time direction S1 (cyan faces) smoothly shrinking to zero size (the bottom row, left panel) In these states the chiral symmetry of the gauge theory is unbroken. Tdbecon — deconfined thermal states with the Euclidean time direction S1 smoothly shrinking to zero size (the bottom row, right panel) It is not practical to publicly release the code and the data produced, as it takes over 150MB
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