Pure partition functions of multiple SLEs

Abstract

Multiple Schramm-Loewner Evolutions (SLE) are conformally invariant random processes of several curves, whose construction by growth processes relies on partition functions: Möbius covariant solutions to a system of second order partial differential equations. In this article, we use a quantum group technique to construct a distinguished basis of solutions, which conjecturally correspond to the extremal points of the convex set of probability measures of multiple SLEs.

47 pages, 15 figures, to appear in Communications in Mathematical Physics

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Cited by in corpus (15)

• Global and Local Multiple SLEs for $\kappa \le 4$ and Connection Probabilities for Level Lines of GFF
• A formula for crossing probabilities of critical systems inside polygons
• Towards a conformal field theory for Schramm-Loewner evolutions
• Connection probabilities for conformal loop ensembles
• Crossing Probabilities of Multiple Ising Interfaces
• Boundary correlations in planar LERW and UST
• UST branches, martingales, and multiple SLE(2)
• N-sided Radial Schramm-Loewner Evolution
• Three phases of multiple SLE driven by non-colliding Dyson's Brownian motions
• Connection Probabilities of Multiple FK-Ising Interfaces
• Statistical Mechanics of Confined Polymer Networks
• Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT
• Multiple Ising interfaces in annulus and $2N$-sided radial SLE
• The quantum group dual of the first-row subcategory for the generic Virasoro VOA
• Planar UST Branches and $c=-2$ Degenerate Boundary Correlations