Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models

Abstract

In this paper we discuss the blackhole-string transition of the small Schwarzschild blackhole of $Ad{S}_5\times S^5$ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak {\it and} strong coupling, can be expressed entirely in terms of constant Polyakov lines which are $SU(N)$ matrices. In showing this we have taken into account that there are no Nambu-Goldstone modes associated with the fact that the 10 dimensional blackhole solution sits at a point in $S^5$. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order $N=\infty$ phase transition with the blackhole-string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of $N^{-2/3}$. The $N=\infty$ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the Lorenztian section of the small Schwarzschild blackhole.

arXiv comment44 pages, Minor changes,the submitted version in the journal

References in corpus (26)

• Eternal Black Holes in AdS
• A Correspondence Principle for Black Holes and Strings
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• EXTREMAL BLACK HOLES AND ELEMENTARY STRING STATES
• The Black Hole Singularity in AdS/CFT
• Exact Counting of Black Hole Microstates
• Inside the Horizon with AdS/CFT
• Precision Counting of Small Black Holes
• Gauge Fields and Space-Time
• A Stringy Cloak for a Classical Singularity
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• A first order deconfinement transition in large N Yang-Mills theory on a small 3-sphere
• Finite temperature effective action, AdS_5 black holes, and 1/N expansion
• Unstable Horizons
• Non-Perturbative Solution of Matrix Models Modified by Trace-Squared Terms
• Accelerating Branes and the String/Black Hole Transition
• A Pendant for Polya: The One-Loop Partition Function of N=4 SYM on R x S^3
• R-charged AdS_{5} black holes and large N unitary matrix models
• Fine structure of Hagedorn transitions
• Rolling Down the Throat in NS5-brane Background: The Case of Electrified D-Brane
• Loop Equations and the Topological Phase of Multi-Cut Matrix Models
• The Charged Black Hole/String Transition
• Beyond the Singularity of the 2-D Charged Black Hole
• D-Brane Propagation in Two-Dimensional Black Hole Geometries
• Thermal Phase Transition in Weakly Interacting Large N_C QCD
• Note on Small Black Holes in AdS_p x S^q

Cited by in corpus (62)

• Black hole thermodynamics from simulations of lattice Yang-Mills theory
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
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• Phases of one dimensional large N gauge theory in a 1/D expansion
• Phase structure of matrix quantum mechanics at finite temperature
• Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$
• Matching the Hagedorn temperature in AdS/CFT
• Phase Transitions in Higher Derivative Gravity
• Free Fermions and Thermal AdS/CFT
• Instabilities of the Small Black Hole: a view from N=4 SYM
• High temperature expansion in supersymmetric matrix quantum mechanics
• Partial Deconfinement
• Phase Transitions of Large N Orbifold Gauge Theories
• Phase transitions in higher derivative gravity and gauge theory: R-charged black holes
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• N=4 SYM on S^3 with Near Critical Chemical Potentials
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• String Stars in Anti de Sitter Space
• Spectral form factor for free large $N$ gauge theory and strings
• Gross-Witten-Wadia transition in a matrix model of deconfinement
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Magnetic Heisenberg-chain/pp-wave correspondence
• Yang-Mills Instantons and Dyons on Group Manifolds
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories
• On an Airy matrix model with a logarithmic potential
• Hedgehog black holes and the Polyakov loop at strong coupling
• Microstates of a $2d$ Black Hole in string theory
• Confinement/Deconfinement Transition of Large N Gauge Theories in Perturbation Theory with N_f Fundamentals: N_f/N Finite
• Finite N Index and Angular Momentum Bound from Gravity
• Thermodynamics of theories with sixteen supercharges in non-trivial vacua
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Duality and replicas for a unitary matrix model
• Dissolved deconfinement: Phase Structure of large N gauge theories with fundamental matter
• Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty )$ gauge theory
• Hagedorn divergences and tachyon potential
• Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT
• Hagedorn Strings and Correspondence Principle in AdS(3)
• Multiple phases and meromorphic deformations of unitary matrix models
• Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
• Plasma balls/kinks as solitons of large $N$ confining gauge theories
• Unitary matrix models and random partitions: Universality and multi-criticality
• Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories
• From Phase Space to Integrable Representations and Level-Rank Duality
• New States of Gauge Theories on a Circle
• Phase Space Distribution of Riemann Zeros
• Black Hole - String Transition and Rolling D-brane
• Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory
• String Theory: A Framework for Quantum Gravity and Various Applications
• Phases of unitary matrix models and lattice QCD2
• Gauge/Gravity Duality and Some Applications
• A note on matrix model with IR cutoff and AdS/CFT
• Notes on relativistic superfluidity and gauge/string duality
• The Plasma Puddle as a Perturbative Black Hole
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory
• Matrix Model For Polyakov Loops, String Field Theory In The Temporal Gauge, Winding String Condensation In Anti-de Sitter Space And Field Theory Of D-branes
• Phase Structure of Beta-deformed N=4 SYM on S^3 with Chemical Potentials
• Hawking-Page transition on a spin chain
• Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential
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• Gauge theory description of the fate of the small Schwarzschild blackhole