Some special points in the moduli space of c=N conformal field theory

The authors point out a generalized Frenkel-Kac point for the c=N conformal field theories in fermion language. The critical value, R=1/√2, of the modular parameter for the c=1 case is generalized to R=1/√N=1 for c=N, where R is a parameter in the moduli space which can be used to continuously deform a conformal field theory with SO(2N)L X SO(2N)R Kac-Moody symmetry to one with SU(N+1)L X SU (N+1)R symmetry. Similar deformation from [SO(N)]L2 X [SO(N)]R2 to SO(N+1)L x SO(N+1)R is also shown to occur at R=1/√N+1