The minimal series of N=1 and N=2 superconformal topological field theory

Abstract

We obtain conformal invariant topological field theories with N=2 supersymmetry by twisting Sevrin, Troost and Van Proeyen's SU (2) × SU (2) × U (1) extended N=4 superconformal field theories. We expect that the number of physical states is finite although the original N=4 theories have continuous spectra. It is shown that the number of physical states is actually finite when the central charge c<6 in the corresponding N=4 theories. The physical states inherit the structure of the chiral ring in N=2 superconformal minimal series which is obtained by the reduction from N=4 theories. We also show that the algebra contains the topological N=4 superconformal algebra as subalgebra. Therefore a closed set of a finite number of physical states in the topological N=1 superconformal algebra can also be obtained.