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arXiv · hep-th/0506046

The Correlator Toolbox, Metrics and Moduli

Robert O. Bauer·Roland M. Friedrich
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Abstract

We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Loewner 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 $\text{SLE}(κ,ρ)$ in terms of conformally invariant random growing compact subsets of polygons. The parameters $ρ_j$ are related to the exterior angles of the polygons. We also show that $\text{SLE}(κ,ρ)$ 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.

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Robert O. Bauer, Roland M. Friedrich. 2005-06-05. The Correlator Toolbox, Metrics and Moduli. https://doi.org/10.1016/j.nuclphysb.2005.10.040

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