HEP Theory Journal Club

Conformal Bootstrap Universality between c>25 and c<1 two-dimensional CFTs

Yiannis Tsiares

IPhT, Saclay

Two-dimensional Conformal Field Theories (CFTs) are special compared to their higher-dimensional cousins due to the extended amount of symmetry captured by the Virasoro algebra. This fact has been proven useful in the analytic conformal bootstrap approach to some extent, yet many interesting questions, such as the space of theories with just Virasoro symmetry and central charge c> 1, remain largely unknown. In this talk, we will attempt to approach those questions by studying an important kinematic object of the conformal bootstrap, the crossing kernels of Virasoro blocks, as an analytic function of the central charge. We will find a surprising relation that connects crossing kernels valid for central charge regimes c>25 and kernels valid for c<1. Among other results, we will use this correspondence to prove analytically that time-like Liouville theory is crossing symmetric and modular covariant. Based on work to appear with Sylvain Ribault.