Degrees of freedom in two dimensional string theory

Abstract

We discuss two issues regarding the question of degrees of freedom in two dimensional string theory. The first issue relates to the classical limit of quantum string theory. In the classical theory one requires an infinite number of fields in addition to the collective field to describe ``folds'' on the fermi surface. We argue that in the quantum theory these are not additional degrees of freedom. Rather they represent quantum dispersions of the collective field which are {\em not} suppressed when $\hslash \to 0$ whenever a fold is present, thus leading to a nontrivial classical limit. The second issue relates to the ultraviolet properties of the geometric entropy. We argue that the geometric entropy is finite in the ultraviolet due to {\em nonperturbative} effects. This indicates that the true degrees of freedom of the two dimensional string at high energies is much smaller than what one naively expects. (Based on talks at Spring Workshop on String theory and Quantum Gravity, ICTP, Trieste, March 1995 and VIIth Regional Conference on Mathematical Physics, Bandar-Anzali, October 1995.)

18 pages, LaTeX

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• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Deep Quantum Geometry of Matrices
• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Entanglement in the Quantum Hall Matrix Model
• Matrix Quantum Mechanics from Qubits
• Entanglement Renormalization and Two Dimensional String Theory
• Finiteness of Entanglement Entropy in Collective Field Theory
• Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
• Emergent Area Laws from Entangled Matrices
• Higher Spin Gravity in $Ad{S}_3$ and Folds on Fermi Surface
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Quantum Quench in $c=1$ Matrix Model and Emergent Space-times
• Scrambling and the black hole atmosphere