Geometrization of the TUY/WZW/KZ connection
Abstract
Given a simple, simply connected, complex algebraic group G, a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic Gbundles over any family of smooth projective curves with marked points was constructed by the authors in an earlier paper. Here, it is shown that the identification between the bundle of nonabelian theta functions and the bundle of WZNW conformal blocks is flat with respect to this connection and the one constructed by TsuchiyaUenoYamada. As an application, we give a geometric construction of the KnizhnikZamolodchikov connection on the trivial bundle over the configuration space of points in the projective line whose typical fiber is the space of invariants of tensor product of representations.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.00430
 Bibcode:
 2021arXiv211000430B
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory;
 Primary: 14H60;
 32G34;
 53D50;
 Secondary: 81T40;
 14F08
 EPrint:
 Preliminary version, 38 pp, comments are welcome!