Discrete and Continuum Virasoro Constraints in Two-Cut Hermitian Matrix Models

Abstract

Continuum Virasoro constraints in the two-cut hermitian matrix models are derived from the discrete Ward identities by means of the mapping from the $GL(\infty )$ Toda hierarchy to the nonlinear Schrödinger (NLS) hierarchy. The invariance of the string equation under the NLS flows is worked out. Also the quantization of the integration constant $α$ reported by Hollowood et al. is explained by the analyticity of the continuum limit.