Status  Confirmed 
Seminar Series  SOUTENTH 
Subjects  physics 
Date  Wednesday 10 October 2018 
Time  14:00 
Institute  IPHT 
Seminar Room  Amphi Claude Bloch, Bât. 774 
Speaker's Last Name  Santiago Migliaccio 
Speaker's First Name  
Speaker's Email Address  
Speaker's Institution  IPhT 
Title  Conformal bootstrap in twodimensional conformal field theories with nondiagonal spectrums 
Abstract  Conformal symmetry imposes very strong constraints on quantum field theories. In two dimensions, the conformal symmetry algebra is infinitedimensional, and twodimensional 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 twodimensional 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 nondiagonal 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 fourpoint functions in diagonal and nondiagonal minimal models, and verifying that crossing symmetry is satisfied. \par In addition, we build a proposal for a family of nondiagonal, nonrational conformal field theories for any central charges such that $\Re{c} < 13$. This proposal is motivated by taking limits of the spectrum of Dseries minimal models. We perform numerical computations of fourpoint functions in these theories, and find that they satisfy crossing symmetry. These theories may be understood as nondiagonal 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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