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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

BOUNDARY TODA CONFORMAL FIELD THEORY FROM THE PATH INTEGRAL

Baptiste Cerclé
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Nathan Huguenin

Résumé

Toda Conformal Field Theories (CFTs hereafter) are generalizations of Liouville CFT where the underlying field is no longer scalar but takes values in a finite-dimensional vector space. The algebra of symmetry of such models is given by W-algebras, which contain the Virasoro algebra as a subalgebra. In contrast with Liouville CFT, and in the presence of a boundary, there may exist non-trivial automorphisms of the associated W-algebra, corresponding to different boundary conditions for the field of the theory. Based on this particular feature, we provide in this document a probabilistic construction of Toda CFTs on a Riemann surface with or without boundary. To be more specific we define different classes of models in relation with the different types of boundary conditions suggested by the non-triviality of the automorphism group of the W-algebra. To do so, we rely on a probabilistic framework based on Gaussian Free Fields and Gaussian Multiplicative Chaos, and make sense of "Cardy's doubling trick" to construct the underlying field of the theory.
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Dates et versions

hal-04634623 , version 1 (04-07-2024)

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Baptiste Cerclé, Nathan Huguenin. BOUNDARY TODA CONFORMAL FIELD THEORY FROM THE PATH INTEGRAL. 2024. ⟨hal-04634623⟩
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