Conformal blocks from vertex algebras and theirconnections on ℳg,n
Chiara Damiolini, Angela Gibney, Nicola Tarasca
Abstract
We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent sheaves on moduli of stable pointed curves. These generalize Verlinde bundles or vector bundles of conformal blocks defined using affine Lie algebras studied first by Tsuchiya-Kanie, Tsuchiya-Ueno-Yamada, and extend work of a number of researchers. The sheaves carry a twisted logarithmic D-module structure, and hence support a projectively flat connection. We identify the logarithmic Atiyah algebra acting on them, generalizing work of Tsuchimoto for affine Lie algebras.
Topics & Concepts
MathematicsVertex operator algebraVertex (graph theory)Pure mathematicsAffine transformationLie conformal algebraAffine Lie algebraConnection (principal bundle)Conformal mapModuli spaceLie algebraVector bundleLogarithmAlgebra over a fieldCombinatoricsAlgebra representationJordan algebraCurrent algebraMathematical analysisGeometryGraphAlgebraic structures and combinatorial modelsNonlinear Waves and SolitonsAlgebraic Geometry and Number Theory