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Note on Schramm-Loewner Evolution for Superconformal Algebras

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Abstract

Using the group-theoretical formulation of Schramm-Loewner evolution (SLE), we propose variants of SLE related to superconformal algebras. The corresponding stochastic differential equation is derived from a random process on an infinite-dimensional Lie group. We consider random processes on a certain kind of groups of superconformal transformations generated by exponentiated elements of the Grassmann envelop of the superconformal algebras. We present a method for obtaining local martingales from a representation of the superconformal algebra after integration over the Grassmann variables.

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Authors and Affiliations

  1. Department of Basic Science, University of Tokyo, Tokyo, Japan

    S. Koshida

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  1. S. Koshida
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Correspondence to S. Koshida.

Additional information

This research was supported by a Grant-in-Aid for JSPS Fellows (Grant No. 17J09658).

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Koshida, S. Note on Schramm-Loewner Evolution for Superconformal Algebras. Theor Math Phys 199, 501–512 (2019). https://doi.org/10.1134/S0040577919040020

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  • DOI: https://doi.org/10.1134/S0040577919040020

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