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Discrete State Moduli of String Theory from c=1 Matrix Model

Avinash Dhar, Gautam Mandal, Spenta R. Wadia

TL;DR

The paper argues that a consistent space-time interpretation of the c=1 matrix model requires fluctuations on both sides of the inverted potential. It introduces average and difference boundary fields φ(τ) and Δ(τ), linking Δ to background metric perturbations and a black-hole-like mass M, and shows the tachyon corresponds to φ while Δ generates new backgrounds; standard tachyon amplitudes in flat space/linear dilaton are reproduced in the Δ→0 limit, while generic Δ yields additional backgrounds aligned with the two-dimensional tachyon-dilaton-graviton effective theory. This provides a framework for a nonperturbative, dynamical space-time background in 2D string theory via the c=1 matrix model and offers insights into quantum gravity and black hole physics. It suggests paths toward a complete nonperturbative formulation of 2D string theory based on the two-sided matrix model.

Abstract

We propose a new formulation of the space-time interpretation of the $c=1$ matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the fermi vacuum on {\sl both sides} of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent nonperturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.

Discrete State Moduli of String Theory from c=1 Matrix Model

TL;DR

The paper argues that a consistent space-time interpretation of the c=1 matrix model requires fluctuations on both sides of the inverted potential. It introduces average and difference boundary fields φ(τ) and Δ(τ), linking Δ to background metric perturbations and a black-hole-like mass M, and shows the tachyon corresponds to φ while Δ generates new backgrounds; standard tachyon amplitudes in flat space/linear dilaton are reproduced in the Δ→0 limit, while generic Δ yields additional backgrounds aligned with the two-dimensional tachyon-dilaton-graviton effective theory. This provides a framework for a nonperturbative, dynamical space-time background in 2D string theory via the c=1 matrix model and offers insights into quantum gravity and black hole physics. It suggests paths toward a complete nonperturbative formulation of 2D string theory based on the two-sided matrix model.

Abstract

We propose a new formulation of the space-time interpretation of the matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the fermi vacuum on {\sl both sides} of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent nonperturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.

Paper Structure

This paper contains 6 sections, 75 equations, 3 figures.

Table of Contents

  1. Introduction and Summary
  2. Review of the Phase Space Formulation of the Matrix Model
  3. The Leg-pole Transformation to String Theory
  4. Transforming fluctuations on both sides of the potential
  5. Effective Low-energy String Theory
  6. Quantum gravity, Black hole physics and Nonperturbative String Theory

Figures (3)

  • Figure 1: Small fluctuation of the fermi surface on only one side of the potential.
  • Figure 2: A part of the fluid fluctuation crosses the $p=-q$ asymptote.
  • Figure 3: A generic initial small-field fluctuation of the fermi surface.