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Conditions aux bords dans des theories conformes non unitaires

Abstract : Our understanding of surface critical phenomena has made the same progress as its bulk counterpart. In particular, in two dimensions, conformally invariant field theories are now extremely powerful tools which are used to describe phase transitions in a non-perturbative way. In this context, the study of surface critical phenomena has produced numerous new exact results, such as boundary critical exponents or correlation functions in several critical models. In this thesis, we are interested in some statistical field theories in two dimensions, with non-local degrees of freedom. For example, polymers in a good solvant are described by such theories. One can try to turn these theories into local ones, but the price to pay is that we get negative or even complex Boltzmann weights: these theories are then non-unitary. We are interested in surface effects, and in finding out which boundary conditions are compatible with conformal invariance in these theories. Our strategy does not involve an axiomatic approach, but rather relies on concrete lattice models which have an interesting scaling limit.
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Submitted on : Friday, January 14, 2011 - 5:27:09 AM
Last modification on : Monday, February 10, 2020 - 6:13:39 PM
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Jerome Dubail. Conditions aux bords dans des theories conformes non unitaires. Physique mathématique [math-ph]. Université Paris Sud - Paris XI, 2010. Français. ⟨tel-00555624⟩

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