SLE_k growth processes and conformal field theories

TL;DR

This paper explores the connection between Schramm-Loewner Evolution (SLE_k) growth processes and conformal field theories, establishing a link through Markov processes and conserved observables in critical phenomena.

Contribution

It generalizes SLE_k growths to Markov processes on the conformal group, linking them to conformal field theories with specific central charges.

Findings

Established a connection between SLE_k processes and conformal field theories.

Identified zero modes as conserved observables in SLE_k processes.

Generalized SLE_k growths to formal Markov processes on the conformal group.

Abstract

SLE_k stochastic processes describe growth of random curves which, in some cases, may be identified with boundaries of two dimensional critical percolating clusters. By generalizing SLE_k growths to formal Markov processes on the central extension of the 2d conformal group, we establish a connection between conformal field theories with central charges c_k=(3k-8)(6/k-1)/2 and zero modes -- observables which are conserved in mean -- of the SLE_k stochastic processes.