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Teichmüller Groupoids, and Monodromy in Conformal Field Theory

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Abstract

We study monodromy representations of the Teichmüller groupoid for the moduli space of pointed compact Riemann surfaces of any genus with first-order infinitesimal structure. To calculate these representations, using arithmetic Schottky-Mumford uniformization theory we construct a real orbifold in the moduli space consisting of fusing and simple moves which gives tangential base points. For a certain vector bundle on the moduli space with projectively flat connection, we show that the monodromy of each fusing move can be expressed as a connection matrix, and give the relations to the monodromy of simple moves. Furthermore, we describe the monodromy representation associated with Tsuchiya-Ueno-Yamada’s conformal field theory, and show that this representation can be expressed as the monodromy of the Wess-Zumino-Witten model.

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  1. Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan

    Takashi Ichikawa

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  1. Takashi Ichikawa
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Correspondence to Takashi Ichikawa.

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Communicated by L. Takhtajan

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Ichikawa, T. Teichmüller Groupoids, and Monodromy in Conformal Field Theory. Commun. Math. Phys. 246, 1–18 (2004). https://doi.org/10.1007/s00220-003-1033-z

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