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

Abstract

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.

Latex, 22 pages

References in corpus (11)

• Interaction of Discrete States in Two-Dimensional String Theory
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Ward Identities in Two-Dimensional String Theory
• On the Liouville Approach to Correlation Functions for 2-D Quantum Gravity
• SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with c < 1 matter
• Genus Zero Correlation Functions in c<1 String Theory
• Correlation Functions of (2k-1, 2) Minimal Matter Coupled to 2D Quantum Gravity
• Ward Identities of $W_{\infty }$ Symmetry in Liouville Theory coupled to $c_M<1$ Matter
• Physical States, Factorization and Nonlinear Structures in Two Dimensional Quantum Gravity
• Ward Identities of Liouville Gravity coupled to Minimal Conformal Matter
• Non-linear Structures in Non-critical NSR String