2000/04/06 by J. Fuchs, Fuchs, J., C. Schweigert +1
Mathematics · Physics and Astronomy · #14D21 #14H60 #81T30 #81T40 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.AG #math.QA #msc:14D21 #msc:14H60 #msc:81T30 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math/0004034
9 pages, LaTeX2e. Invited contribution to the 3rd ECM, Barcelona, July 2000
arxiv created 2000/04/06 · arxiv updated 2009/11/30
Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply a Verlinde formula for non-simply connected groups like PGL(n,C). We then explain how conformal blocks enter in the construction of conformal field theories on surfaces with boundaries. Such surfaces naturally appear in the conformal field theory description of string propagation in the background of a D-brane. In this context, the sub-bundle structure of the conformal blocks controls the structure of symmetry breaking boundary conditions.