Virasoro constraints of multi-matric model and chern-simons theories on SO(N) and Sp(2N)

Abstract

We have obtained a unique extension of Virasoro constraint operators to negative modes which satisfy the full virasoro algebra without using any new parameters. These unique new operators give the central charge which reflects the geometric structure of the coupling constant space. The central charge of N-matrix model which is related to 2-dimensional su(N+1) topological field theory turns out to be N. Also, We obtain the skein relations for link polynomials from the Chern-Simons theories on SO(N) and Sp(2N), using E. Witten``s method which he has used in order to obtain such a relation for Jones polynomial in the case of SU(N). We show that for SO(N) and Sp(2N), these polynomials are related to the Dubrovnik polynomial.