Abstract
An abelian 4D, \( \mathcal{N} \) = 4 vector supermultiplet allows for a duality transformation to be applied to one of its spin-0 states. The resulting theory can be described as an abelian 4D, \( \mathcal{N} \) = 4 vector-tensor supermultiplet. It is seen to decompose into a direct sum of an off-shell 4D, \( \mathcal{N} \) = 2 vector supermultiplet and an off-shell 4D, \( \mathcal{N} \) = 2 tensor supermultiplet. The commutator algebra of the other two supersymmetries are still found to be on-shell. However, the central charge structure in the resulting 4D, \( \mathcal{N} \) = 4 vector-tensor supermultiplet is considerably simpler that that of the parent abelian 4D, \( \mathcal{N} \) = 4 vector supermultiplet. This appears to be due to the replacement of the usual SO(4) symmetry associated with the abelian 4D, \( \mathcal{N} \) = 4 vector supermultiplet being replaced by a GL(2,\( \mathbb{R} \))⊗GL(2,\( \mathbb{R} \)) symmetry in the 4D, \( \mathcal{N} \) = 4 vector-tensor supermultiplet. The Mathematica code detailing the calculations is available open-source at the HEPTHoolsData Repository on GitHub.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.K. Das, SO(4) invariant extended supergravity, Phys. Rev. D 15 (1977) 2805 [INSPIRE].
E. Cremmer and J. Scherk, Algebraic simplifications in supergravity theories, Nucl. Phys. B 127 (1977) 259 [INSPIRE].
E. Cremmer, J. Scherk and S. Ferrara, SU(4) invariant supergravity theory, Phys. Lett. B 74 (1978) 61.
F. Gliozzi, J. Scherk and D.I. Olive, Supersymmetry, supergravity theories and the dual spinor model, Nucl. Phys. B 122 (1977) 253 [INSPIRE].
L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills theories, Nucl. Phys. B 121 (1977) 77 [INSPIRE].
M. Sohnius, K.S. Stelle and P.C. West, Off mass shell formulation of extended supersymmetric gauge theories, Phys. Lett. B 92 (1980) 123.
W. Siegel, Off-shell central charges, Nucl. Phys. B 173 (1980) 51 [INSPIRE].
P. Claus et al., The vector-tensor supermultiplet with gauged central charge, Phys. Lett. B 373 (1996) 81 [hep-th/9512143] [INSPIRE].
P. Claus, P. Termonia, B. de Wit and M. Faux, Chern-Simons couplings and inequivalent vector-tensor multiplets, Nucl. Phys. B 491 (1997) 201 [hep-th/9612203] [INSPIRE].
P. Claus et al., N = 2 supergravity Lagrangians with vector tensor multiplets, Nucl. Phys. B 512 (1998) 148 [hep-th/9710212] [INSPIRE].
N. Dragon, S.M. Kuzenko and U. Theis, The vector-tensor multiplet in harmonic superspace, Eur. Phys. J. C 4 (1998) 717 [hep-th/9706169] [INSPIRE].
N. Dragon and S.M. Kuzenko, Selfinteracting vector-tensor multiplet, Phys. Lett. B 420 (1998) 64 [hep-th/9709088] [INSPIRE].
P. Claus et al., Vector tensor multiplets, Fortsch. Phys. 47 (1999) 125 [hep-th/9801200] [INSPIRE].
S.J. Gates Jr. et al., An extended detailed investigation of first and second order supersymmetries for off-shell \( \mathcal{N} \) = 2 and \( \mathcal{N} \) = 4 supermultiplets, Symmetry 7 (2015) 1080 [arXiv:1106.5475].
S.J. Gates Jr. and K. Stiffler, Adinkra ‘color’ confinement in exemplary off-shell constructions of 4D, \( \mathcal{N} \) = 2 supersymmetry representations, JHEP 07 (2014) 051 [arXiv:1405.0048] [INSPIRE].
J. Wess, Fermi-Bose supersymmetry, Lect. Notes Phys. 37 (1975) 352 [INSPIRE].
P. Fayet, Fermi-Bose hypersymmetry, Nucl. Phys. B 113 (1976) 135 [INSPIRE].
S.J. Gates Jr. and L. Rana, A theory of spinning particles for large N extended supersymmetry, Phys. Lett. B 352 (1995) 50 [hep-th/9504025] [INSPIRE].
S.J. Gates Jr. and L. Rana, A theory of spinning particles for large N extended supersymmetry. 2., Phys. Lett. B 369 (1996) 262 [hep-th/9510151] [INSPIRE].
M. Faux and S.J. Gates Jr., Adinkras: a graphical technology for supersymmetric representation theory, Phys. Rev. D 71 (2005) 065002 [hep-th/0408004] [INSPIRE].
S.J. Gates Jr. et al., 4D, N = 1 supersymmetry genomics (I), JHEP 12 (2009) 008 [arXiv:0902.3830] [INSPIRE].
S.J. Gates Jr. et al., 4D, N = 1 supersymmetry genomics (II), JHEP 06 (2012) 071 [arXiv:1112.2147] [INSPIRE].
S.J. Gates Jr., J. Hallett, T. Hubsch and K. Stiffler, The real anatomy of complex linear superfields, Int. J. Mod. Phys. A 27 (2012) 1250143 [arXiv:1202.4418] [INSPIRE].
I. Chappell et al., 4D, N = 1 supergravity genomics, JHEP 10 (2013) 004 [arXiv:1212.3318] [INSPIRE].
S.J. Gates Jr., T. Hübsch and K. Stiffler, Adinkras and SUSY Holography: Some explicit examples, Int. J. Mod. Phys. A 29 (2014) 1450041 [arXiv:1208.5999] [INSPIRE].
S.J. Gates Jr., T. Hübsch and K. Stiffler, On Clifford-algebraic dimensional extension and SUSY holography, Int. J. Mod. Phys. A 30 (2015) 1550042 [arXiv:1409.4445] [INSPIRE].
M. Calkins, D.E.A. Gates, S.J. Gates Jr. and K. Stiffler, Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence, Int. J. Mod. Phys. A 30 (2015) 1550050 [arXiv:1501.00101] [INSPIRE].
S.J. Gates Jr. et al., A Lorentz covariant holoraumy-induced “gadget” from minimal off-shell 4D, \( \mathcal{N} \) = 1 supermultiplets, JHEP 11 (2015) 113 [arXiv:1508.07546] [INSPIRE].
D.E.A. Gates, S.J. Gates Jr. and K. Stiffler, A proposal on culling & filtering a coxeter group for 4D, \( \mathcal{N} \) = 1 spacetime SUSY representations: revised, JHEP 08 (2016) 076 [arXiv:1601.00725] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1812.04236
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gates, S.J., Stiffler, K. Exploring the abelian 4D, \( \mathcal{N} \) = 4 vector-tensor supermultiplet and its off-shell central charge structure. J. High Energ. Phys. 2019, 129 (2019). https://doi.org/10.1007/JHEP03(2019)129
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2019)129