Minkowski superspaces and superstrings as almost real-complex supermanifolds
S Bouarroudj, PY Grozman, DA Leites… - Theoretical and …, 2012 - Springer
S Bouarroudj, PY Grozman, DA Leites, IM Shchepochkina
Theoretical and mathematical physics, 2012•SpringerFor 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.
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.
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.
Springer