Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

Details Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

1994-11-02

arxiv.org/abs/hep-th/9411014v1

Phys.Rev. D51 (1995) 6959-6969

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 22 pages

Scientific paper

10.1103/PhysRevD.51.6959

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.

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