Date of Award

8-1-2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Physics

Content Description

1 online resource (xi, 129 pages) : illustrations

Dissertation/Thesis Chair

Daniel Robbins

Committee Members

Eric Sharpe, Oleg Lunin, Ariel Caticha, Herbert Fotso

Keywords

Conformal mapping, Orbifolds, Arakelov theory, Riemann surfaces

Subject Categories

Other Physics

Abstract

We examine conformal field theories and their gaugings (orbifolds), first on the torus and then on surfaces of higher genus. Specific attention is paid to performing explicit calculations, to which end we introduce a number of specialized formalisms. Namely, the technology of flavored partition functions allows for a general treatment of orbifolds in theories with conserved currents, and Arakelov geometry facilitates the derivation of novel expressions for geometric quantities appearing commonly on higher genus worldsheets. Ultimately, we leverage the resulting expressions in the calculation of correlation functions via degeneration of Riemann surfaces.

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