N=1 SUPERCONFORMAL MINIMAL MODEL CORRELATION FUNCTIONS ON THE TORUS

Abstract

The Coulomb gas formalism is employed to construct contour integral representations of two-point correlation functions on the torus for the N=1 superconformal unitary discrete series, characterized by the single integer p. (For the particular case of the tricritical Ising model, these include the energy and vacancy density operators.) Modular and monodromy properties of the superconformal blocks are examined, and the generalization to superconformal theories of Verlinde’s results on modular transformations and the fusion algebra are discussed in some detail. For p odd the relevant modular matrix is (with respect to a particular basis) symmetric and unitary, as in ordinary rational conformal theory. However, for p even, there appears to be an obstruction due to the Ramond vacuum state.