String Beta Function Equations From c=1 Matrix Model

Abstract

We derive the $\sigma$-model tachyon $\beta$-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the $c=1$ matrix model. The tachyon $\beta$-function equation is satisfied by a \underbar{nonlocal} and \underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the $c=1$ matrix model. We also comment on the realization of the $W$-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the $c=1$ matrix model.

18 pages, latex, no figures (typos corrected, version to appear in Nucl Phys. B)

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Cited by in corpus (8)

• Fermions from Half-BPS Supergravity
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• Spacelike boundaries from the c=1 Matrix Model
• Discrete State Moduli of String Theory from c=1 Matrix Model
• The emergence of space-time gravitational physics as an effective theory from the c=1 matrix model
• Rolling tachyon solution of two-dimensional string theory
• Fermions in the harmonic potential and string theory
• Into the bulk: reconstructing spacetime from the c=1 matrix model