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dc.contributor.advisorTuite, Michael
dc.contributor.authorWelby, Michael
dc.description.abstractIn 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.en_IE
dc.publisherNUI Galway
dc.subjectvertex operator algebrasen_IE
dc.subjectRiemann surfacesen_IE
dc.subjectZhu reductionen_IE
dc.subjectdifferential formsen_IE
dc.subjectMathematics, Statistics and Applied Mathematicsen_IE
dc.titleZhu reduction theory for vertex operator algebras on Riemann surfacesen_IE
dc.contributor.funderIrish Research Councilen_IE
dc.local.noteA Vertex Operator Algebra (VOA) is a mathematical version of string theory. We consider recursion formulas for correlation functions in multiloop string theory on a Riemann surface either formed by joining two one-loop surfaces or by joining a sphere to itself multiple times for a superVOA or a VOA respectively.en_IE

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