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Conformal bootstrap in two-dimensional conformal field theories with with non-diagonal spectrums

Abstract : 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.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.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.
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Submitted on : Friday, November 16, 2018 - 12:14:06 PM
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  • HAL Id : tel-01924845, version 1

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Santiago Migliaccio. Conformal bootstrap in two-dimensional conformal field theories with with non-diagonal spectrums. High Energy Physics - Experiment [hep-ex]. Université Paris Saclay (COmUE), 2018. English. ⟨NNT : 2018SACLS362⟩. ⟨tel-01924845⟩

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