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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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\paper Minkowski superspaces and superstrings as almost real--complex supermanifolds
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  • https://www.mathnet.ru/eng/tmf/v173/i3/p416
    • This publication is cited in the following 7 articles:
    1. Bruce A.J., Grabowski J., “Odd Connections on Supermanifolds: Existence and Relation With Affine Connections”, J. Phys. A-Math. Theor., 53:45 (2020), 455203  crossref  mathscinet  isi
    2. D. A. Leites, “Two problems in the theory of differential equations”, Theoret. and Math. Phys., 198:2 (2019), 271–283  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. Alldridge, “Frechet globalisations of Harish-Chandra supermodules”, Int. Math. Res. Notices, 2017, no. 17, 5182–5232  crossref  mathscinet  isi
    4. A. Altomani, A. Santi, “Classification of maximal transitive prolongations of super-Poincaré algebras”, Adv. Math., 265 (2014), 60–96  crossref  mathscinet  zmath  isi
    5. A. Alldridge, J. Hilgert, T. Wurzbacher, “Singular superspaces”, Math. Z., 278:1-2 (2014), 441–492  crossref  mathscinet  zmath  isi
    6. S. Bouarroudj, V. Ovsienko, “Riemannian Curl in Contact Geometry”, International Mathematics Research Notices, 2014  crossref
    7. Alexander Alldridge, Zain Shaikh, Springer INdAM Series, 7, Advances in Lie Superalgebras, 2014, 1  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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