John Cardy
Published 2003-01-28, updated 2003-11-11Version 4
Stochastic Loewner Evolution (SLE_kappa) has been introduced as a description of the continuum limit of cluster boundaries in two-dimensional critical systems. We show that the problem of N radial SLEs in the unit disc is equivalent to Dyson's Brownian motion on the boundary of the disc, with parameter beta=4/kappa. As a result various equilibrium critical models give realisations of circular ensembles with beta different from the classical values of 1,2 and 4 which correspond to symmetry classes of random U(N) matrices. Some of the bulk critical exponents are related to the spectrum of the associated Calogero-Sutherland hamiltonian. The main result is also checked against the predictions of conformal field theory.
Comments: 8 pages. v.2: main result confirmed using conformal field theory; subtle square root elucidated; figures added. v.3: funding acknowledgements added. v.4: erratum to published paper added: this exposes more fully the relation to CFT results
Journal: J. Phys. A 36, L379, 2003; erratum J.Phys. A, 36, 12343, 2003
Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model
Conformal field theory at central charge c=0: a measure of the indecomposability (b) parameters
Non-Equilibrium Conformal Field Theories with Impurities
