Vertex algebras of CohFT-type

15 Jul 2020  ·  Damiolini Chiara, Gibney Angela, Tarasca Nicola ·

Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple cohomological field theories... As an application, we give an expression for their total Chern character in terms of the fusion rules, following the approach and computation in [MOPPZ] for bundles given by integrable modules over affine Lie algebras. It follows that the Chern classes are tautological. Examples and open problems are discussed. read more

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Algebraic Geometry Quantum Algebra