Études des fonctions de corrélation en théorie conforme des champs : transformation intégrale du développement en produit d'opérateurs

Authors: Bélanger, Mathieu
Advisor: Fortin, Jean-François
Abstract: Correlation functions in conformal eld theory can be expressed with the help of the operator product expansion. The latter contains all the necessary information to characterize those theories. This expansion has given rise to the bootstrap equations. The bootstrap program has led to interesting numerical results but analytic equivalents have yet to be found. Some recent results introduced the inversion formula to the operator product expansion which allows one to nd the conformal data for the correlation function. Those relations need the complete form of the correlation function which are not usually known. This renders those inversion formulas hard to use for the bootstrap program. Here, we propose an integral transformation of the operator product expansion that uses the inversion formula. This gives us a way to relate the conformal data of the different crossing symmetry channels. In the case of four identical scalar elds, this relation can be used as a recurrence relation in two and four dimensions. This might validate known results and also nd some new systems.
Document Type: Mémoire de maîtrise
Issue Date: 2020
Open Access Date: 14 February 2020
Permalink: http://hdl.handle.net/20.500.11794/38112
Grantor: Université Laval
Collection:Thèses et mémoires

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