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Zhu reduction theory for vertex operator algebras on Riemann surfaces

Welby, Michael
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2019-08-21
Keywords
vertex operator algebras, Riemann surfaces, Zhu reduction, differential forms, Mathematics, Statistics and Applied Mathematics, Mathematics
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Thesis
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Abstract
In this thesis we first develop a recursive relation for $n$-point functions for Vertex Operator Super Algebras (VOSAs) on a genus two Riemann surface constructed by sewing two tori. This relation is used to develop formal differential equations for $n$-point functions on a genus two surface, as well as for differential forms on this surface. We demonstrate the applications of this results for a well-known example of VOSA and compare them to existing results in the literature. In the second part, we develop a more general version of this identity for a Vertex Operator Algebra (VOA) on a general genus Riemann surface, using the Schottky uniformisation of a genus $g$ Riemann surface; we then develop some geometric theory for the results that arise. We also apply this results to well-known examples of VOAs to obtain general genus identities for objects such as differential forms on a Riemann surface.
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Irish Research Council
Publisher
NUI Galway
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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University of Galway Theses (PhD Theses)