Two-point spin- 12-spin-12 ŝl (2, C) conformal Kac-Moody blocks on the torus and their monodromies Original Research Article

Two issues of the SU(2) Wess-Zumino-Witten model are examined here, namely the computation of the untwisted conformal Kac-Moody blocks on the torus and their monodromy representations. Using the free field representation developed by Bernard and Felder, an integral representation of the twisted two point spin-12-spin-12 conformal Kac-Moody blocks on the torus is computed. From this, an integral representation of the untwisted blocks is computed after careful removal of infinities. Finally, the untwisted blocks are used to get a representation of the Braid Group on the torus on two strings, in terms of quantum group q-numbers.