Minkowski superspaces and superstrings as almost real-complex supermanifolds

S. Bouarroudj, P. Ya Grozman, D. A. Leites, I. M. Shchepochkina

Research output: Contribution to journalArticlepeer-review


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{pipe}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.

Original languageEnglish (US)
Pages (from-to)1687-1708
Number of pages22
JournalTheoretical and Mathematical Physics
Issue number3
StatePublished - Dec 2012


  • Kähler supermanifold
  • Nijenhuis tensor
  • complex supermanifold
  • hyper-Kähler supermanifold
  • nonholomorphic distribution
  • real supermanifold
  • string theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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