Speaker:  Bertrand Eynard (IPHT - Saclay)

Abstract: ConformaL Field Theory (CFT) in 2-dimensions, can be characterized by some necessary conditions called bootstrap axioms (behaviors at short distance, conformal invariance, univaluedness of correlation functions...). The problem is rather existence of a solution to these axioms. We shall show how Topological Recursion (TR) provides a solution (as formal perturbative series). The initial condition of the TR is a spectral curve, and here we choose as spectral curve the semiclassical limit of the Stress-Energy-Tensor. The states of the CFT are related to cycles (generalized cycles) on the spectral curve. This cycle formalism admits a non-perturbative counterpart as generalized Goldman cycles in the adjoint bundle of a Fuchsian connection (whose semiclassical limit is a Higgs field whose characteristic polynomial is the spectral curve). This allows to relate to the geometry of the DeRham moduli space. All the formalism also generalizes easily to non-Fuchsian meromorphic connections, and can be used to define irregular conformal blocks.