SLE martingales and the Virasoro algebra

Abstract

We present an explicit relation between representations of the Virasoro algebra and polynomial martingales in stochastic Loewner evolutions (SLE). We show that the Virasoro algebra is the spectrum generating algebra of SLE martingales. This is based on a new representation of the Virasoro algebra, inspired by the Borel-Weil construction, acting on functions depending on coordinates parametrizing conformal maps.

13 pages, to appear in Phys. Lett. B

References in corpus (2)

• SLE_k growth processes and conformal field theories
• Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems

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