Ward Identities of $W_{\infty }$ Symmetry in Liouville Theory coupled to $c_M<1$ Matter

Abstract

We investigate the Ward identities of the $W_{\infty }$ symmetry in the Liouville theory coupled to the $(p,q)$ conformal matter. The correlation functions are defined by applying the analytic continuation procedure for the matter sector as well as the Liouville one. We then find that the Ward identities are equivalent to the $W_q$ algebra constraints deduced from the matrix model.

10 pages, Latex file, YITP/U-93-34

References in corpus (5)

• 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
• SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with c < 1 matter
• Ward Identities of Liouville Gravity coupled to Minimal Conformal Matter

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• Ward Identities of W_{\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory
• Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules