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

TL;DR

This paper derives explicit formulas for two-point functions of primary operators in the SU(2) Wess-Zumino-Witten model on a torus, demonstrating their monodromy and differential equation solutions.

Contribution

It provides explicit current block expressions for all levels k, advancing the understanding of two-point functions in the SU(2) WZW model on the torus.

Findings

Explicit current blocks for all k levels derived.

Confirmed monodromy properties of the current blocks.

Proved solutions satisfy Knizhnik-Zamolodchikov-like equations.

Abstract

We discuss a class of two-point functions on the torus of primary operators in the SU(2) Wess-Zumino-Witten model at integer level k. In particular, we construct an explicit expression for the current blocks of the spin-k/2-spin-k/2 torus two-point functions for all k. We first examine the factorization limits of the proposed current blocks and test their monodromy properties. We then prove that the current blocks solve the corresponding Knizhnik-Zamolodchikov-like differential equations using the method of Mathur, Mukhi and Sen.