Explicit construction of unitary representations of the N = 2 superconformal algebra

Abstract

A representation based on free fermions has been found, realizing the unitary representations of N = 2 superconformal theory when the central charge, c 2, is between 0 and 1. The results confirm previous conjectures for the list of discrete values of c 2 and the superconformal dimensions, h, for highest-weight states with t = 0 in the Neveu-Schwarz sector (and t = ±1 4 in the Ramond sector). Here t is the eigenvalue of the U(1) Kac-Moody current in the theory. For t ≠ 0 ( ±1 4 ) new results are obtained, including a list of possible discrete t-values and a modified list of the possible discrete h-values.