Field identification fixed points in N = 2 coset theories

Abstract

We discuss N = 2 coset models with fixed points in their field identification. We determine the corrections to the modular transformations that are needed to resolve the fixed point, and show how to obtain the correct fusion rules. Furthermore we obtain the complete set of chiral Ramond ground states for the grassmannian coset models, and compute the resulting string spectra (number of generations N g and anti-generations N a for diagonal invariants. A useful tool in these computations is the Poincaré polynomial of the chiral ring, extended with an extra variable to characterize the intersection of the spinor current orbit and the chiral ring. For the non-grassmannian coset theories it is straightforward to compute the Poincaré polynomial, but there is an additional technical complication in obtaining the extended polynomial. We show how to circumvent this problem and obtain N g and N a also for tensor products of these cosets.