arXiv:hep-th/9508009v1 3 Aug 1995 OU-HET 218 YITP/U-95-29 August, 1995 Macroscopic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model 1 M. Anazawa † 2 , A. Ishikawa ‡ 2 and H. Itoyama † † Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka, 560 Japan and ‡ Uji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University, Uji, Kyoto, 611 Japan Abstract From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop am- plitudes having boundary lengths ℓ i (i =1 ∼ 3) in the case of the unitary series (p, q)=(m +1,m) coupled to two-dimensional gravity. The sum ap- pearing 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. 1 This work is supported in part by Grant-in-Aid for Scientific Research (07640403) and by the Grand-in-Aid for Scientific Research Fund (2690, 5108) from the Ministry of Education, Science and Culture, Japan. 2 JSPS fellow