Exact correlation functions in the Brownian Loop Soup
Abstract
We compute analytically and in closed form the fourpoint correlation function in the plane, and the twopoint correlation function in the upper halfplane, of layering vertex operators in the two dimensional conformally invariant system known as the Brownian Loop Soup. These correlation functions depend on multiple continuous parameters: the insertion points of the operators, the intensity of the soup, and the charges of the operators. In the case of the fourpoint function there is nontrivial dependence on five continuous parameters: the crossratio, the intensity, and three real charges. The fourpoint function is crossing symmetric. We analyze its conformal block expansion and discover a previously unknown set of new conformal primary operators.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2020
 DOI:
 10.1007/JHEP07(2020)067
 arXiv:
 arXiv:1912.00973
 Bibcode:
 2020JHEP...07..067C
 Keywords:

 Conformal Field Theory;
 Integrable Field Theories;
 Random Systems;
 Stochastic Processes;
 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematics  Probability
 EPrint:
 28 pages, 2 figures