Skip to main content
SpringerLink
Log in

Stochastic Evolutions in Superspace and Superconformal Field Theory

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu–Schwarz sector.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schramm, O.: Scaling limits of loop-erased random walks and uniform spanning trees, Israel J. Math. 118 (2000), 221–288.

    Google Scholar 

  2. Lawler, G. L., Schramm, O. and Werner, W.: Values of Brownian intersection exponents. I. Half-plane exponents, Acta Math. 187 (2001), 237–273; Values of Brownian intersection exponents. II. Plane exponents, Acta Math. 187 (2001), 275–308; Values of Brownian intersection exponents. III. Two-sided exponents, Ann. Inst. Henri Poincaré Probab. Statist. 38 (2002), 109–123; Conformal restriction: the cordal case, math.PR/0209343.

    Google Scholar 

  3. Rohde, S. and Schramm, O.: Basic properties of SLE, math.PR/0106036.

  4. Bauer, M. and Bernard, D.: SLEk growth processes and conformal field theories, Phys. Lett. B 543 (2002), 135–138; Conformal field theories of stochastic Löwner evolutions, Comm. Math. Phys. 239 (2003), 493–521.

    Google Scholar 

  5. Friederich, R. and Werner, W.: Conformal restriction, highest-weight representations and SLE, math-ph/0301018.

  6. Lesage, F. and Rasmussen, J.: SLE-type growth processes and the Yang–Lee singularity, math-ph/0307058.

  7. Rogers, A.: Supersymmetry and Brownian motion on supermanifolds, quant-ph/0201006.

  8. Dörrzapf, M.: The definition of Neveu–Schwarz superconformal fields and uncharged superconformal transformations, Rev. Math. Phys. 11 (1999), 137–169.

    Google Scholar 

  9. Nagi, J.: Superconformal primary fields on a graded Riemann sphere, hepth/0309243.

Download references

Author information

Authors and Affiliations

  1. Centre de recherches mathématiques, Université de Montréal, Case postale 6128, succursale centre-ville, Qc, Canada)

    Jørgen Rasmussen

Authors
  1. Jørgen Rasmussen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rasmussen, J. Stochastic Evolutions in Superspace and Superconformal Field Theory. Letters in Mathematical Physics 68, 41–52 (2004). https://doi.org/10.1007/s11005-004-5100-y

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-004-5100-y

Search

Navigation