×

Quaternionic (super) twistors extensions and general superspaces. (English) Zbl 1356.81152

Summary: In an attempt to treat a supergravity as a tensor representation, the four-dimensional \(N\)-extended quaternionic superspaces are constructed from the (diffeomorphic) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [Int. J. Geom. Methods Mod. Phys. 13, No. 9, Article ID 1650113, 10 p. (2016; Zbl 1352.32005)], with \(N=p+k\). These quaternionic superspaces have \(4+k(N-k)\) even-quaternionic coordinates and \(4N\) odd-quaternionic coordinates, where each coordinate is a quaternion composed by four \(\mathbb{C}\)-fields (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case, the number of fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional \(N\)-extended quaternionic superspaces. The role of tensorial central charges for any \(N\) even \(U\mathrm{Sp}(N)=\mathrm{Sp}(N,\mathbb{H}_{\mathbb{C}})\cap U(N,\mathbb{H}_{\mathbb{C}})\) is elucidated from this theoretical context.

MSC:

81R25 Spinor and twistor methods applied to problems in quantum theory
81R30 Coherent states
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
11R52 Quaternion and other division algebras: arithmetic, zeta functions
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
32C11 Complex supergeometry
83E50 Supergravity

Citations:

Zbl 1352.32005
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] A. B. Borisov and V. I. Ogievetsky, Theoret. Math. Phys.21 (1975) 1179 [Teoret. Mat. Fiz.21 (1974) 329-342 (in Russian)].
[2] S. R. Coleman, J. Wess and B. Zumino, Phys. Rev.177 (1969) 2239; D. V. Volkov, Fiz. Elem. Chastits. At. Yadra4 (1973) 3; D. V. Volkov, Preprint ITF 6973 (Inst. Teor. Fiz., Kiev, 1969).
[3] Penrose, R., Quantum Gravity, eds. Isham, C. J., Penrose, R. and Sciama, D. W. (Clarendon Press, Oxford, 1965), p. 268.
[4] Ogievetsky, V. I., Lett. Nuovo Cimento8 (1973) 988.
[5] Cirilo-Lombardo, D. J. and Pervushin, V. N., Int. J. Geom. Methods Mod. Phys.13 (2016) 1650113.
[6] Litov, L. B. and Pervushin, V. N., Phys. Lett. B147 (1984) 76.
[7] Ogievetsky, V. and Sokatchev, E., Phys. Lett. B79 (1978) 222.
[8] Lukierski, J. and Nowicki, A., Phys. Lett. B211 (1988) 276.
[9] Nonlinear Problems in Mathematical Physics and Related Topics I: In Honour of Prof. O. A. Ladyzhenskaiya, eds. Birman, M. Sh.et al. (Kluwer/Plenum Publishers, 2002).
[10] Ferber, A., Nuclear Phys. B132 (1978) 55.
[11] Cirilo-Lombardo, D. J., Int. J. Theor. Phys.54(10) (2015) 3713-3727.
[12] D. J. Cirilo-Lombardo and A. B. Arbuzob, Quaternionic super-extensions of the supertwistor construction: Super-analog of the Borisov-Ogievetsky nonlinear realization, work in progress.
[13] Morita, K., Prog. Theor. Phys.117 (2007) 501-532.
[14] Cirilo-Lombardo, D. J. and Pervushin, V. N., Int. J. Geom. Methods Mod. Phys.131650113 (2016) 10 pages, doi: http://dx.doi.org/10.1142/S0219887816501139.
[15] Lukierski, J. and Nowicki, B., Moderen Phys. Lett. A6 (1991) 189.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.