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

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

1995-08-03

arxiv.org/abs/hep-th/9508009v1

Phys.Lett. B362 (1995) 59-64

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, no figure, latex

Scientific paper

10.1016/0370-2693(95)01180-X

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.

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