The Exact $S$-matrix of the Deformed $c=1$ Matrix Model

Abstract

We consider the $c=1$ matrix model deformed by the operator ${1\over 2} M\TrΦ^{-2}$, which was conjectured by Jevicki and Yoneya to describe a two-dimensional black hole of mass $M$. We calculate the exact non-perturbative $S$-matrix and show that all the amplitudes involving an odd number of particles vanish at least to all orders of perturbation theory. We conjecture that these amplitudes vanish non-perturbatively and prove this for the $2n\to 1$ scattering. For the 2-- and 4--particle amplitudes we give some leading terms of the perturbative expansion.

arXiv comment8 pages, uses phyzzx, PUPT-1416, CNLS-93-09

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• String Theory in Two Dimensions
• Exact S-Matrix for 2D String Theory
• A Deformed Matrix Model and the Black Hole Background in Two-Dimensional String Theory
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• Matrix Models and Black Holes
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• Condensing Momentum Modes in 2-d 0A String Theory with Flux
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