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Full-Text Articles in Physics
Calculational Methods In Conformal Field Theory, Thomas Andrew Vandermeulen
Calculational Methods In Conformal Field Theory, Thomas Andrew Vandermeulen
Legacy Theses & Dissertations (2009 - 2024)
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.
Conformal Field Theory And Its Application To The Ising Model, Joshua Edward Meyer
Conformal Field Theory And Its Application To The Ising Model, Joshua Edward Meyer
Legacy Theses & Dissertations (2009 - 2024)
The two-dimensional Ising model was originally solved by Onsager using statistical physics techniques. More recently, it has been found that the derivation of critical exponents and correlation functions can be greatly simplified by using the methods of Conformal Field Theory (CFT). We review these methods and apply them to the two-dimensional Ising model. The connection between the continuum limit Ising model and the field theory of free fermions is explained, resulting in a CFT on the plane with two non-trivial fields. Through the use of bosonization on the plane, the free-field correlation functions of the model are computed.