String Beta Function Equations From c=1 Matrix Model

Details String Beta Function Equations From c=1 Matrix Model String Beta Function Equations From c=1 Matrix Model

1995-03-24

arxiv.org/abs/hep-th/9503172v2

Nucl.Phys. B451 (1995) 507-524

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(95)00319-N

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.

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