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Chiral Ring Structure in the N = 2 Superconformal Field Theory Based on the Coset Construction with SU(1,1)/U(1)

In this paper, we carefully analyze the unitarity of the simplest Kazama–Suzuki model based on the noncompact group. The chiral ring structure in this N = 2 theory is clarified. In general, it is infinitely dimensional and innumerable. The primary chiral states belonging to the ring can be constructed by means of the direct products of the highest weight states of the coset SU(1,1)/U(1) and the scalar representation of U(1) for the fermions. The primary chird and anti-chiral states live individually in the positive discrete series D+ and negative discrete series D- of SU(1,1), respectively. With appropriate restrictions, this theory can be regarded as one at the fixed point of a Landau–Ginzburg theory, in which the superpotential is given by S12 in the fourteen exceptional singularities.