The correlator toolbox, metrics and moduli

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 s...

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Bibliographic Details
Published in:Nuclear physics. B 2006-01, Vol.733 (1), p.91-103
Main Authors: Bauer, Robert O., Friedrich, Roland M.
Format: Article
Language:English
Subjects:
Conformal field theory
Probability theory
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Summary: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 growing 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 ρ j 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.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2005.10.040