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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 3, Pages 416–440
DOI: https://doi.org/10.4213/tmf6872 (Mi tmf6872) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Minkowski superspaces and superstrings as almost real–complex supermanifolds

S. Bouarroudja, P. Ya. Grozmanb, D. A. Leitesc, I. M. Shchepochkinad

a New York University Abu Dhabi, Division of Science and Mathematics, Abu Dhabi, U.A.E.
b Equa Simulation AB, Stockholm, Sweden
c Department of Mathematics, Stockholm University, Stockholm, Sweden
d Independent University of Moscow, Moscow, Russia
Full-text PDF (653 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf6872
Abstract: For the Minkowski superspace and superstrings, we define and compute a circumcised analogue of the Nijenhuis tensor, the obstruction to the integrability of an almost real–complex structure. The Nijenhuis tensor vanishes identically only if the superstring superdimension is $1|1$ and, moreover, the superstring is endowed with a contact structure. We also show that all real forms of Grassmann algebras are isomorphic, although they are defined by obviously different anti-involutions.
Keywords: real supermanifold, complex supermanifold, Nijenhuis tensor, string theory, nonholomorphic distribution, Kähler supermanifold, hyper-Kähler supermanifold.
Received: 02.05.2010
Revised: 10.06.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 3, Pages 1687–1708
DOI: https://doi.org/10.1007/s11232-012-0141-3
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. Bouarroudj, P. Ya. Grozman, D. A. Leites, I. M. Shchepochkina, “Minkowski superspaces and superstrings as almost real–complex supermanifolds”, TMF, 173:3 (2012), 416–440; Theoret. and Math. Phys., 173:3 (2012), 1687–1708
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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