Macroscopoic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model

Abstract

From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop amplitudes having boundary lengths ${\ell }_i$ $(i=1\sim 3)$ in the case of the unitary series $(p,q)=(m+1,m)$ coupled to two-dimensional gravity. The sum appearing in this expression is found to conform to the structure of the CFT fusion rules while the summand factorizes through a product of three modified Bessel functions. We briefly discuss a possible generalization of these features to macroscopic $n$-loop amplitudes.

9 pages, no figure, latex

References in corpus (4)

• Rational Theories of 2D Gravity from the Two-Matrix Model
• Strings with Discrete Target Space
• Superloop Equations and Two Dimensional Supergravity
• 2D Quantum Gravity in the Proper-Time Gauge

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• Boundary operators and touching of loops in 2d gravity
• Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory