Minkowski superspaces and superstrings as almost real-complex supermanifolds

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

doi:10.1007/s11232-012-0141-3

Minkowski superspaces and superstrings as almost real-complex supermanifolds

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1687-1708
Number of pages	22
Journal	Theoretical and Mathematical Physics
Volume	173
Issue number	3
DOIs	https://doi.org/10.1007/s11232-012-0141-3
State	Published - Dec 2012

Keywords

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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10.1007/s11232-012-0141-3

Cite this

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title = "Minkowski superspaces and superstrings as almost real-complex supermanifolds",

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.",

keywords = "K{\"a}hler supermanifold, Nijenhuis tensor, complex supermanifold, hyper-K{\"a}hler supermanifold, nonholomorphic distribution, real supermanifold, string theory",

author = "S. Bouarroudj and Grozman, {P. Ya} and Leites, {D. A.} and Shchepochkina, {I. M.}",

note = "Funding Information: This work was supported in part (S. B.) by New York University Abu Dhabi (Grant No. AD 065).",

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AU - Bouarroudj, S.

AU - Grozman, P. Ya

AU - Leites, D. A.

AU - Shchepochkina, I. M.

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AB - 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.

KW - Kähler supermanifold

KW - Nijenhuis tensor

KW - complex supermanifold

KW - hyper-Kähler supermanifold

KW - nonholomorphic distribution

KW - real supermanifold

KW - string theory

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JO - Theoretical and Mathematical Physics

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ER -

Minkowski superspaces and superstrings as almost real-complex supermanifolds

Abstract

Keywords

ASJC Scopus subject areas

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