Continuum Annulus Amplitude from the Two-Matrix Model

Abstract

An explicit expression for continuum annulus amplitudes having boundary lengths ${\ell }_1$ and ${\ell }_2$ is obtained from the two-matrix model for the case of the unitary series; $(p,q)=(m+1,m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m=2(c=0)$ and the $m\to \infty (c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.

9 pages, OU-HET 190, revised version. A part of the conclusions has been corrected. A new result on integral representation of the annulus amplitudes has been added

References in corpus (6)

• Rational Theories of 2D Gravity from the Two-Matrix Model
• Strings with Discrete Target Space
• Superloop Equations and Two Dimensional Supergravity
• Touching Random Surfaces and Liouville Gravity
• 2D Quantum Gravity in the Proper-Time Gauge
• Wheeler-DeWitt Equation in Two-dimensional Quantum Gravity with $c=1$ Conformal Matter Field

Cited by in corpus (6)

• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Boundary operators in minimal Liouville gravity and matrix models
• Macroscopic $n$-Loop Amplitude for Minimal Models Coupled to Two-Dimensional Gravity: Fusion Rules and Interactions
• Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory
• Boundary operators and touching of loops in 2d gravity