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SUSY Vertex Algebras and Supercurves

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Given a strongly conformal SUSY vertex algebra V and a supercurve X, we construct a vector bundle \({\fancyscript V}^r_X\) on X, the fiber of which is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle \({\fancyscript V}^r_X\), corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.

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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Reimundo Heluani

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  1. Reimundo Heluani
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Correspondence to Reimundo Heluani.

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Communicated by Y. Kawahigashi

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Heluani, R. SUSY Vertex Algebras and Supercurves. Commun. Math. Phys. 275, 607–658 (2007). https://doi.org/10.1007/s00220-007-0325-0

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  • DOI: https://doi.org/10.1007/s00220-007-0325-0

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