Minkowski superspaces and superstrings as almost real-complex supermanifolds

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

Research output: Contribution to journalArticle

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{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
Volume173
Issue number3
DOIs
StatePublished - Dec 1 2012

Fingerprint

Supermanifold
Superspaces
Superstring
Nijenhuis Tensor
tensors
vector spaces
Grassmann Algebra
electric contacts
Contact Structure
analogs
Obstruction
Complex Structure
Involution
Integrability
Vanish
Isomorphic
Analogue

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Minkowski superspaces and superstrings as almost real-complex supermanifolds. / Bouarroudj, Sofiane; Grozman, P. Ya; Leites, D. A.; Shchepochkina, I. M.

In: Theoretical and Mathematical Physics, Vol. 173, No. 3, 01.12.2012, p. 1687-1708.

Research output: Contribution to journalArticle

Bouarroudj, Sofiane ; Grozman, P. Ya ; Leites, D. A. ; Shchepochkina, I. M. / Minkowski superspaces and superstrings as almost real-complex supermanifolds. In: Theoretical and Mathematical Physics. 2012 ; Vol. 173, No. 3. pp. 1687-1708.
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