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Twisted Logarithmic Modules of Vertex Algebras

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Abstract

Motivated by logarithmic conformal field theory and Gromov–Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted fields involve the logarithm of the formal variable. We develop the theory of such twisted modules and, in particular, derive a Borcherds identity and commutator formula for them. We investigate in detail the examples of affine and Heisenberg vertex algebras.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Bojko Bakalov

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  1. Bojko Bakalov
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Correspondence to Bojko Bakalov.

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Communicated by Y. Kawahigashi

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Bakalov, B. Twisted Logarithmic Modules of Vertex Algebras. Commun. Math. Phys. 345, 355–383 (2016). https://doi.org/10.1007/s00220-015-2503-9

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  • DOI: https://doi.org/10.1007/s00220-015-2503-9

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