Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines physics
Date Mercredi 10 Octobre 2018
Heure 14:00
Institut IPHT
Salle Amphi Claude Bloch, Bât. 774
Nom de l'orateur Santiago Migliaccio
Prenom de l'orateur
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Institution de l'orateur IPhT
Titre Conformal bootstrap in two-dimensional conformal field theories with non-diagonal spectrums
Résumé Conformal symmetry imposes very strong constraints on quantum field theories. In two dimensions, the conformal symmetry algebra is infinite-dimensional, and two-dimensional conformal field theories can be completely solvable, in the sense that all their correlation functions may be computed. These theories have an ample range of applications, from string theory to critical phenomena in statistical physics, and they have been widely studied during the last decades. \par In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic conformal bootstrap method to theories with non-diagonal spectrums. We write the equations that determine structure constants, and find explicit solutions in terms of special functions. We validate this results by numerically computing four-point functions in diagonal and non-diagonal minimal models, and verifying that crossing symmetry is satisfied. \par In addition, we build a proposal for a family of non-diagonal, non-rational conformal field theories for any central charges such that $\Re{c} < 13$. This proposal is motivated by taking limits of the spectrum of D-series minimal models. We perform numerical computations of four-point functions in these theories, and find that they satisfy crossing symmetry. These theories may be understood as non-diagonal extensions of Liouville theory. \\ \\ (Sylvain Ribault, directeur de thèse ; Valentina Petkova, rapporteur ; Oleg Lisovyy, rapporteur ; Pascal Baseilhac, examinateur ; Raoul Santachiara, examinateur ; Yacine Ikhlef, examinateur.)
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