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We discuss a class of two-point functions on the torus of primary operatorsin the SU(2) Wess-Zumino-Witten model at integer level k. In particular, weconstruct an explicit expression for the current blocks of thespin-k/2-spin-k/2 torus two-point functions for all k. We first examine thefactorization limits of the proposed current blocks and test their monodromyproperties. We then prove that the current blocks solve the correspondingKnizhnik-Zamolodchikov-like differential equations using the method of Mathur,Mukhi and Sen.

Spin-k/2-spin-k/2 SU(2) two-point functions on the torus