The Correlator Toolbox, Metrics and Moduli
Robert O. Bauer, Roland M. Friedrich

TL;DR
This paper develops a framework for generalized SLE processes using boundary conformal field theories, emphasizing the role of moduli and geometric interpretations involving polygons and gravitational backgrounds.
Contribution
It introduces a set of operators for boundary CFTs to construct generalized SLE($, ho$), highlighting the importance of moduli and providing a geometric derivation involving polygons and gravitational coupling.
Findings
Generalized SLE($, ho$) can be derived from boundary CFT operators.
Moduli are essential for a consistent kinematic description of these processes.
A geometric interpretation relates parameters _j to polygon exterior angles.
Abstract
We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Loewner type procedure to generalisations of SLE(). We also highlight the necessity of moduli for a consistent kinematic description of these more general stochastic processes. As an illustration we give a geometric derivation of in terms of conformally invariant random growing compact subsets of polygons. The parameters are related to the exterior angles of the polygons. We also show that can be generated by a Brownian motion in a gravitational background, where the metric and the Brownian motion are coupled. The metric is obtained as the pull-back of the Euclidean metric of a fluctuating polygon.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
