Nonsinglet Sector of $c=1$ Matrix Model and 2D Black Hole

Abstract

Extending our recent work (\arXiv{\tt hep-th/0310106}) we study the nonsinglet sector of $c=1$ matrix model by renormalization group analysis for a gauged matrix quantum mechanics on circle with an appropriate gauge breaking term to incorporate the effect of world-sheet vortices. The flow equations indicate BKT phase transition around the self-dual radius and the nontrivial fixed points of the flow exhibit black hole like phases for a range of temperatures beyond the self-dual point. One class of fixed point interpolate between $c=1$ for $R>1$ and $c=0$ as $R\to 0$ via black hole phase that emerges after the phase transition. The other two classes of nontrivial fixed points also develop black hole like behavior beyond R=1. From a thermodynamic study of the free energy obtained from the Callan-Symanzik equations we show that all these unstable phases do have negative specific heat. The thermodynamic quantities indicate that the system does undergo a first order phase transition near the Hagedorn temperature, around which the new phase is formed, and exhibits one loop finite energy correction to the Hagedorn density of states. The flow equations also suggest a deformation of the target space geometry through a running of the compactification radius where the scale is given by the dilaton. Remarkably there is a regime where cyclic flow is observed.

arXiv comment54 pages, 10 figures

References in corpus (17)

• A Matrix Model for the Two Dimensional Black Hole
• Strings from Tachyons
• Classical and Quantum D-branes in 2D String Theory
• The Annular Report on Non-Critical String Theory
• Non-Perturbative Effects in Matrix Models and D-branes
• One-Dimensional String Theory with Vortices as Upside-Down Matrix Oscillator
• A Deformed Matrix Model and the Black Hole Background in Two-Dimensional String Theory
• A Note on Background (In)dependence
• Stringy Quantum Effects in 2-Dimensional Black-Hole
• Black hole formation in $c=1$ String Field Theory
• Matrix Models and One Dimensional Open String Theory (Revised)
• Renormalization Group Approach to $c=1$ Matrix Model on a circle and D-brane Decay
• Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces
• Matrix Models and Nonperturbative String Propagation in Two-Dimensional Black Hole Backgrounds
• The emergence of space-time gravitational physics as an effective theory from the c=1 matrix model
• The Two-Dimensional O(2) Model on a Random Planar Lattice at Strong Coupling
• Two Dimensional String Theory And Black Holes

Cited by in corpus (8)

• Liouville Field Theory -- A decade after the revolution
• Flux Backgrounds in 2D String Theory
• Anatomy of Deconfinement
• Matrix Models, Integrable Structures, and T-duality of Type 0 String Theory
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• Hidden symmetries and Large N factorisation for permutation invariant matrix observables
• 2D Black Hole and Holographic Renormalization Group
• De Sitter Quantum Mechanics and Inflationary Matrix Cosmology of Self-tuned Universe