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The orthosymplectic supergroup is the sub-supergroup of the general linear supergroup on those elements which preserve the canonical graded-symmetric bilinear form on , i.e. the form which is the canonical symmetric bilinear form on the even elements , is the canonical symplectic form on the odd elements in and is zero on mixed pairs of elements.
The corresponding super Lie algebras are called the orthosymplectic Lie algebras . Over a field of characteristic zero these constitute the infinite - and -series in the classification of simple super Lie algebras. They are closely related to superconformal symmetry (e.g. D’Auria-Ferrara-Lledo-Varadarajan 00), see at supersymmetry – Classification – Superconformal symmetry.
is a limiting case of the M-theory super Lie algebra (Fernandez-Izquierdo-Olmo 15).
Further relation also to the type II supersymmetry algebra had been discussed in (Bergshoess-Proeyen 00).
The M-theory super Lie algebra is actually a sub-super Lie algebra of (vanHolten-VanProeyen 82, Bars-Deliduma-nMinic 99, (11)-(15), West 00, section 7)
In fact is the smallest simple supergroup that contains the M-theory super Lie algebra. Moreover, it is generated from its M-theory sub-algebra and the special conformal transformations (Bars-Deliduman-Minic 99, p. 5)
The super anti de Sitter spacetimes are quotients of orthosymplectic super Lie groups:
super anti de Sitter spacetime | |
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4 | |
5 | |
7 |
Victor Kac, pages 9-10 of A sketch of Lie superalgebra theory, Comm. Math. Phys. Volume 53, Number 1 (1977), 31-64. (EUCLID)
Manfred Scheunert, chapter II, 4.3.A of The theory of Lie superalgebras. An introduction, Lect. Notes Math. 716 (1979)
Richard Joseph Farmer, Orthosymplectic superalgebras in mathematics and science, PhD Thesis (1984) (web, pdf)
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, section II.2.2 in Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
Riccardo D'Auria, S. Ferrara, M. A. Lledó, Veeravalli Varadarajan, Spinor Algebras, J.Geom.Phys. 40 (2001) 101-128 (arXiv:hep-th/0010124)
N. A. Gromov, I. V. Kostyakov, V. V. Kuratov, Cayley-Klein contractions of orthosymplectic superalgebras (arXiv:hep-th/0110257)
Steven V Sam, Orthosymplectic Lie superalgebras, Koszul duality, and a complete intersection analogue of the Eagon-Northcott complex (arXiv:1312.2255)
G.I. Lehrer, R.B. Zhang, The second fundamental theorem of invariant theory for the orthosymplectic supergroup (arXiv:1407.1058)
Appearance of sl(2)-modular functor is found in the seemingly plain sl(2)-WZW model for fractional level (see there) in:
Igor Bandos, Jerzy Lukierski, Christian Preitschopf, Dmitri Sorokin, OSp supergroup manifolds, superparticles and supertwistors, Phys.Rev.D61:065009, 2000 (arXiv:hep-th/9907113)
Eric Bergshoeff, Antoine Van Proeyen, The many faces of , Class. Quantum Grav. 17 (2000) 3277–3303 (arXiv:hep-th/0003261)
Horatiu Nastase, Towards a Chern-Simons M theory of (arXiv:hep-th/0306269)
J.J. Fernandez, J.M. Izquierdo, M.A. del Olmo, Contractions from to the M-theory superalgebra extended by additional fermionic generators, Nuclear Physics B Volume 897, August 2015, Pages 87–97 (arXiv:1504.05946)
Jan-Willem van Holten, Antoine Van Proeyen, Supersymmetry Algebras in , , , J.Phys. A15 (1982) 3763 (spire:177060)
Itzhak Bars, C. Deliduman, D. Minic, Lifting M-theory to Two-Time Physics, Phys.Lett. B457 (1999) 275-284 (arXiv:hep-th/9904063)
Itzhak Bars, 2T Physics Formulation of Superconformal Dynamics Relating to Twistors and Supertwistors, Phys.Lett. B483 (2000) 248-256 (arXiv:hep-th/0004090)
Peter West, Hidden Superconformal Symmetry in M Theory, JHEP 0008:007, 2000 (arXiv:hep-th/0005270)
The representation theory (singleton representations) of the orthosymplectic group is discussed in
Last revised on May 5, 2023 at 10:58:54. See the history of this page for a list of all contributions to it.