On stochastic evolutions and superconformal field theory. (English) Zbl 1119.81386
Summary: Links between certain stochastic evolutions of conformal maps and conformal field theory have been studied in the realm of SLE and by utilizing singular vectors in highest-weight modules of the Virasoro algebra. It was recently found that this scenario could be extended to stochastic evolutions of 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. Here we discuss the analogous extension to the Ramond sector. We also discuss how the links are modified when an unconventional superconformal structure or superderivative is employed.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 58C50 | Analysis on supermanifolds or graded manifolds |
| 60H99 | Stochastic analysis |
References:
| [1] | Schramm, O., Israel J. Math., 118, 221 (2000) · Zbl 0968.60093 |
| [2] | Lawler, G. F.; Schramm, O.; Werner, W., Conformal restriction: the cordal case |
| [3] | Rohde, S.; Schramm, O., Basic properties of SLE · Zbl 1081.60069 |
| [4] | Bauer, M.; Bernard, D., Commun. Math. Phys., 239, 493 (2003) · Zbl 1046.81091 |
| [5] | Friederich, R.; Werner, W., Conformal restriction, highest-weight representations and SLE · Zbl 1030.60095 |
| [6] | Lesage, F.; Rasmussen, J., SLE-type growth processes and the Yang-Lee singularity, J. Math. Phys., 45, 3040 (2004) · Zbl 1071.82044 |
| [7] | Rasmussen, J., Stochastic evolutions in superspace and superconformal field theory, Lett. Math. Phys., in press · Zbl 1056.81067 |
| [8] | Rogers, A., Supersymmetry and Brownian motion on supermanifolds · Zbl 1067.81080 |
| [9] | Kac, V. G.; van de Leur, J. W., On classification of superconformal algebras, (Gates, S. J.; Preitschopf, C. R.; Siegel, W., Strings ’88 (1989), World Scientific), 77-106 · Zbl 0938.17500 |
| [10] | Nagi, J., J. Math. Phys., 45, 2492 (2004) · Zbl 1071.81094 |
| [11] | Dörrzapf, M., Rev. Math. Phys., 11, 137 (1999) · Zbl 1073.81650 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
