Schramm–Loewner-evolution-type growth processes corresponding to Wess–Zumino–Witten theories

  • Shinji KoshidaEmail author


A group theoretical formulation of Schramm–Loewner-evolution-type growth processes corresponding to Wess–Zumino–Witten theories is developed that makes it possible to construct stochastic differential equations associated with more general null vectors than the ones considered in the most fundamental example in Alekseev et al. (Lett Math Phys 97:243–261, 2011). Also given are examples of Schramm–Loewner-evolution-type growth processes associated with null vectors of conformal weight 4 in the basic representations of \(\widehat{\mathfrak {sl}}_{2}\) and \(\widehat{\mathfrak {sl}}_{3}\).


Schramm–Loewner evolution Wess–Zumino–Witten theory Conformal field theory 

Mathematics Subject Classification

60J67 81T40 17B67 



The author is grateful to K. Sakai and R. Sato for fruitful discussions. This work was supported by a Grant-in-Aid for JSPS Fellows (Grant No. 17J09658).


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Authors and Affiliations

  1. 1.Department of Basic ScienceThe University of TokyoTokyoJapan

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