Michel Bauer, Denis Bernard
SLE$_\kappa$ Growth Processes and Conformal Field Theories
Preprint series: ESI preprints

MSC:

60J65 Brownian motion, See also {58G32}

81T40 Two-dimensional field theories, conformal field theories, etc.

22E65 Infinite-dimensional Lie groups and their Lie algebras, See also {17B65, 58B25, 58H05}

PACS: 02.50.-r;05.40.-a;11.25.Hf;02.20.Tw
Abstract: $SLE_\kappa$ stochastic processes describe growth of random curves
which, in some cases, may be identified with boundaries of two
dimensional critical percolating clusters. By generalizing
$SLE_\kappa$ growths to formal Markov processes on the central
extension of the 2d conformal group, we establish a connection
between conformal field theories with central charges
$c_\kappa=\frac{1}{2}(3\kappa-8)(\frac{6}{\kappa}-1)$ and zero modes
-- observables which are conserved in mean -- of the $SLE_\kappa$
stochastic processes.