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Conformal Field Theory, Automorphic Forms and Related Topics pp 227–246Cite as

Twisted Correlation Functions on Self-sewn Riemann Surfaces via Generalized Vertex Algebra of Intertwiners

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Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 8))

Abstract

We review our recent results on computation of the partition and n-point “intertwined” functions for modules of vertex operator superalgebras with formal parameter associated to local parameters on Riemann surfaces obtained by self-sewing of a lower genus Riemann surface. We introduce the torus intertwined n-point functions containing two intertwining operators in the supertrace. Then we define the partition and n-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by self-sewing of the torus. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from the original torus Szegő kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possess natural modular properties. We describe modularity of the generating function for all n-point correlation functions in terms of a genus two Szegő kernel determinant.

To Proceeding of the Conference: “Conformal Field Theory, Automorphic Forms and Related Topics”, Heidelberg Universität, Heidelberg, Germany, 2011

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Acknowledgements

The author would like to express his deep gratitude to the organizers of the Conference “Conformal Field Theory, Automorphic Forms and Related Topics”, Heidelberg Universität, Heidelberg, Germany, 2011.

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Authors and Affiliations

  1. Max–Planck Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Alexander Zuevsky

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  1. Alexander Zuevsky
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Correspondence to Alexander Zuevsky .

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Editors and Affiliations

  1. University of Heidelberg, Department of Mathematics, Heidelberg, Germany

    Winfried Kohnen

  2. University of Heidelberg, Department of Mathematics, Heidelberg, Germany

    Rainer Weissauer

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Zuevsky, A. (2014). Twisted Correlation Functions on Self-sewn Riemann Surfaces via Generalized Vertex Algebra of Intertwiners. In: Kohnen, W., Weissauer, R. (eds) Conformal Field Theory, Automorphic Forms and Related Topics. Contributions in Mathematical and Computational Sciences, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43831-2_8

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