Fanny Eustachon: Long-range minimal models

mercredi 12 nov. 2025, 14:00 → 15:00 Europe/Paris

I will present a class of nonlocal conformal field theories (CFTs) in 2d which are obtained as deformations of the Virasoro minimal models. The construction proceeds by coupling a relevant primary operator $\phi_{r,s}$ of the m-th minimal model to a generalized free field. Flowing to the infrared, we reach a new class of CFTs that we call long-range minimal models (LRMMs). During this talk, I will discuss two specific types of LRMMs in the framework of conformal perturbation theory: the case r=s=2 corresponding to a straightforward generalization of an infrared duality between the deformed minimal model and a nonlocal Ginzburg-Landau theory proposed for the long-range Ising model ($m = 3$) in 2017, as well as the case (r,s)=(1,2) endowed with a well-behaved large m-limit obtained from both numerical extrapolations and a method we develop which carries out conformal perturbation theory using Mellin amplitudes and Coulomb gas representations of the correlators. This is based on https://arxiv.org/abs/2509.26372