CFTs of SLEs: the radial case

TL;DR

This paper establishes a new connection between conformal field theories and radial SLEs, using Virasoro algebra representations to construct martingales and analyze their properties.

Contribution

It extends the CFT-SLE correspondence to the radial case, providing methods to compute derivative exponents and restriction martingales.

Findings

Constructed local martingales using Virasoro algebra

Linked SLE dual Fokker-Planck operator to Calogero Hamiltonian

Outlined computation of derivative exponents and restriction martingales

Abstract

We present a relation between conformal field theories (CFT) and radial stochastic Schramm-Loewner evolutions (SLE) similar to that we previously developed for the chordal SLEs. We construct an important local martingale using degenerate representations of the Virasoro algebra. We sketch how to compute derivative exponants and the restriction martingales in this framework. In its CFT formulation, the SLE dual Fokker-Planck operator acts as the two-particle Calogero hamiltonian on boundary primary fields and as the dilatation operator on bulk primary fields localized at the fixed point of the SLE map.