Abstract
We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilsons line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g>0 Riemann surfaces depend only on those for g⩽3.
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