Modular invariance for the N = 2 twisted superconformal algebra

The authors study the modular invariance properties of two-dimensional N = 2 twisted superconformal invariant field theories. They express the character of the unitarizable highest weight representations with central charge c = 1 - 2/m, m = 2,3,..., in terms of certain θ - functions with characteristics. The authors give the modular transformations of the characters and obtain the modular invariance structures. The structures differ in the cases m = 0 mod 4 and m = 2 mod 4, while the cases of mod are subcases of 4m. The latter is illustrated for m = 3