TY - JOUR
T1 - The correlator toolbox, metrics and moduli
AU - Bauer, Robert O.
AU - Friedrich, Roland M.
N1 - Funding Information:
R.F. would like to thank Shoibal Chakravarty for the questions asked and the discussions. Gastón Giribert he thanks for helpful explanations. John Cardy he thanks for discussing the notes and for general discussions. The research of the first author was supported by NSA grant H98230-04-1-0039. The research of the second author was supported by a grant of the Max-Planck-Gesellschaft.
PY - 2006/1/16
Y1 - 2006/1/16
N2 - We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Löwner type procedure to generalisations of SLE (κ, ρ). We also highlight the necessity of moduli for a consistent kinematic description of these more general stochastic processes. As an illustration we give a geometric derivation of SLE(κ, ρ) in terms of conformally invariant random growinginf compact subsets of polygons. Further, we also mention a related class of polyhedral SLE (κ, ρ, ρ) processes. In the case of polygons, the parameters ρj are related to the exterior angles. We also show that SLE (κ, ρ) can be generated by a Brownian motion in a gravitational background, where the metric and the Brownian motion are coupled. The metric is obtained as the pull-back of the Euclidean metric of a fluctuating polygon.
AB - We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Löwner type procedure to generalisations of SLE (κ, ρ). We also highlight the necessity of moduli for a consistent kinematic description of these more general stochastic processes. As an illustration we give a geometric derivation of SLE(κ, ρ) in terms of conformally invariant random growinginf compact subsets of polygons. Further, we also mention a related class of polyhedral SLE (κ, ρ, ρ) processes. In the case of polygons, the parameters ρj are related to the exterior angles. We also show that SLE (κ, ρ) can be generated by a Brownian motion in a gravitational background, where the metric and the Brownian motion are coupled. The metric is obtained as the pull-back of the Euclidean metric of a fluctuating polygon.
KW - Conformal field theory
KW - Probability theory
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U2 - 10.1016/j.nuclphysb.2005.10.040
DO - 10.1016/j.nuclphysb.2005.10.040
M3 - Article
AN - SCOPUS:29144511516
SN - 0550-3213
VL - 733
SP - 91
EP - 103
JO - Nuclear Physics B
JF - Nuclear Physics B
IS - 1-2
ER -