Abelian Conformal Field theories and Determinant Bundles

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dc.creatorAndersen, Jorgen Ellegaard
dc.creatorUeno, Kenji
dc.date2003-04-10
dc.date2006-11-08
dc.date.accessioned2026-07-07T11:10:38Z
dc.date.available2026-07-07T11:10:38Z
dc.descriptionThe present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichmüller space of an oriented pointed surface gives the vectorspace the modular functor associates to the oriented pointed surface. However the connection on the sheaf of vacua is only projectively flat, so we need to find a suitable line bundle with a connection, such that the tensor product of the two has a flat connection. We shall construct a line bundle with a connection on any family of pointed curves with formal coordinates. By computing the curvature of this line bundle, we conclude that we actually need a fractional power of this line bundle so as to obtain a flat connection after tensoring. In order to functorially extract this fractional power, we need to construct a preferred section of the line bundle. We shall construct the line bundle by the use of the so-called $bc$-ghost systems (Faddeev-Popov ghosts) first introduced in covariant quantization [FP]. We follow the ideas of [KNTY], but decribe it from the point of view of [TUY].
dc.descriptionA couple of typos corrected
dc.identifierhttps://arxiv.org/abs/math/0304135
dc.identifierhttp://arxiv.org/abs/math/0304135
dc.identifierInt.J.Math.18:919-993,2007
dc.identifierdoi:10.1142/S0129167X07004369
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190836
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.titleAbelian Conformal Field theories and Determinant Bundles
dc.typetext

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