Unitarity Relations in c=1 Liouville Theory

Abstract

We consider the S-matrix of c=1 Liouville theory with vanishing cosmological constant. We examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the plus tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, we show the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. We conclude with some comments about the genus one (N,2) amplitudes.

14 pages, 3 figures (not included), phyzzx

Cited by in corpus (6)

• Lectures on 2D gravity and 2D string theory (TASI 1992)
• Gravitational Scattering in the c = 1 Matrix Model
• On the Nonperturbative Consistency of $d=2$ String Theory
• Discrete State Moduli of String Theory from c=1 Matrix Model
• String Beta Function Equations From c=1 Matrix Model
• Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications