2021/02/11 by Oleg Alekseev, Alekseev, Oleg
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2102.05974
26 pages, 5 figures; v2: typos corrected
arxiv created 2021/02/14 · arxiv updated 2021/02/16
We consider a loop representation of the O(n) model at the critical point. When n=0 the model represents ensembles of self-avoiding loops (i.e., it corresponds to SLE with κ=8/3), and can be described by the logarithmic conformal field theory (LCFT) with central charge c=0. We focus on the correlation functions in the upper-half plane containing the twist operators in the bulk, and a pair of the boundary one-leg operators. By using a Coulomb gas representation for the correlation functions, we obtain explicit results for probabilities of the SLE8/3 trace to wind in various ways about N≥ 1 marked points. When the points collapse pairwise the probabilities reduce to multi-point Green's functions. We propose an explicit representation for the Green's functions in terms of the correlation functions of the bulk 1/3-weight operators, and a pair of the boundary one-leg operators.