Sylvain Lacroix (ETH Zurich)

Sigma-models are two-dimensional field theories which find applications in various domains of physics, such as string theory, holography and condensed matter. A particularly remarkable subclass of these models are the integrable ones, which possess an infinite number of symmetries / conserved charges, allowing for the derivation of exact results. Although this property is well-understood at the classical level, one of the main open challenge in the field is to prove the quantum integrability of these models by first principles, i.e. the explicit construction and the exact diagonalisation of an infinite number of commuting conserved operators at the quantum level. One of the possible approach to simplify this question is to start with the quantum integrability of the UV fixed point of these models, for which we can make use of the algebraic formalism of two-dimensional conformal field theories. In this talk I will report on work in progress with A. Molines on the application of this program to the Wess-Zumino-Novikov-Witten model and in particular on the construction of higher-spin commuting local charges in this conformal theory.