Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT

Understand

We find explicit SLE(8) partition functions for the scaling limits of Peano curves in the uniform spanning tree (UST) in topological polygons with general boundary conditions.

• They are given in terms of Coulomb gas integral formulas, which can also be expressed in terms of determinants involving a-periods of a hyperelliptic Riemann surface.
• We also identify the crossing probabilities for the UST Peano curves as ratios of these partition functions.
• The partition functions are interpreted as correlation functions in a logarithmic conformal field theory (log-CFT) of central charge $c= -2$.