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The KZB equations on Riemann surfaces | | Giovanni Felder
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18 Sep 1996 | | Subject: | hep-th | | Affiliation: | D-MATH, ETH Zuerich | | Abstract: | In this paper, based on the author’s lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan--Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at $n$ marked points are given. The covariant derivatives are expressed in terms of ``dynamical $r$-matrices’’, a notion borrowed from integrable systems. The case of marked points moving on a fixed Riemann surface is studied more closely. We prove a universal form of the (projective) flatness of the connection: the covariant derivatives commute as differential operators with coefficients in the universal enveloping algebra -- not just when acting on conformal blocks. | | Source: | arXiv, hep-th/9609153 | | Services: | Forum | Review | PDF | Favorites | |
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