This article is cited in 7 papers

Minkowski superspaces and superstrings as almost real–complex supermanifolds

S. Bouarroudj^a, P. Ya. Grozman^b, D. A. Leites^c, I. M. Shchepochkina<sup>d

a</sup> 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

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

DOI: 10.4213/tmf6872

 English version: Theoretical and Mathematical Physics, 2012, 173:3, 1687–1708

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