A Brownian Loop Soup based Conformal Field Theory

Gandolfi Alberto, New York University Abu Dhabi

In this talk, we summarize several articles and new results which introduce a conformal field theory whose primary operators based on counting the outer contours of loops from the Brownian Loop Soup (BLS). The resulting fields are conformally covariant and constitute a simplified version of other conformally invariant fields that have been recently extracted from the BLS. Nonetheless, they represent a rather explicit example of a conformal field theory in which several correlation functions can be computed to various degrees of exactness. In particular, several explicit scaling dimensions and three- and four-point function constants are obtained by comparison with the O(n) model and the scaling limit of percolation. The general expression of n-point functions involves SLE Green functions.

Area: CS57 - Statistical Mechanics and applications (Tobias Kuna)

Keywords: Brownian Loop Soup, conformal field theory, SLE, conformal invariance

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