Multiple SLEs describe several random interfaces consistent with conformal symmetries. I will implement a version of conformal field theory constructed from background charge modifications of Gaussian free field and insertion of N-leg operators with screening to show that this version produces a collection of martingale-observables for commuting multiple SLEs. I will explain how this theory is related to its classical limit counterpart, "Loewner Dynamics for Real Rational Functions and the Multiple SLE(0) Process," presented by Tom Alberts in "Introductory Workshop: The Analysis and Geometry of Random Spaces."

Based on joint work with Tom Alberts and Nikolai Makarov.