×

zbMATH — the first resource for mathematics

Exploring the abelian 4D, \( \mathcal{N} \) = 4 vector-tensor supermultiplet and its off-shell central charge structure. (English) Zbl 1414.81238
Summary: 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 \(\mathrm{GL}(2 \mathbb{R}) \otimes \mathrm{GL}(2 \mathbb{R}) \) 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.
MSC:
81T60 Supersymmetric field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Das, AK, SO(4) invariant extended supergravity, Phys. Rev., D 15, 2805, (1977)
[2] Cremmer, E.; Scherk, J., Algebraic simplifications in supergravity theories, Nucl. Phys., B 127, 259, (1977)
[3] Cremmer, E.; Scherk, J.; Ferrara, S., SU(4) invariant supergravity theory, Phys. Lett., B 74, 61, (1978)
[4] Gliozzi, F.; Scherk, J.; Olive, DI, Supersymmetry, supergravity theories and the dual spinor model, Nucl. Phys., B 122, 253, (1977)
[5] Brink, L.; Schwarz, JH; Scherk, J., Supersymmetric Yang-Mills theories, Nucl. Phys., B 121, 77, (1977)
[6] Sohnius, M.; Stelle, KS; West, PC, Off mass shell formulation of extended supersymmetric gauge theories, Phys. Lett., B 92, 123, (1980)
[7] Siegel, W., Off-shell central charges, Nucl. Phys., B 173, 51, (1980)
[8] Claus, P.; etal., The vector-tensor supermultiplet with gauged central charge, Phys. Lett., B 373, 81, (1996)
[9] Claus, P.; Termonia, P.; Wit, B.; Faux, M., Chern-Simons couplings and inequivalent vector-tensor multiplets, Nucl. Phys., B 491, 201, (1997) · Zbl 0925.81255
[10] Claus, P.; etal., N = 2 supergravity Lagrangians with vector tensor multiplets, Nucl. Phys., B 512, 148, (1998) · Zbl 1006.83071
[11] Dragon, N.; Kuzenko, SM; Theis, U., The vector-tensor multiplet in harmonic superspace, Eur. Phys. J., C 4, 717, (1998)
[12] Dragon, N.; Kuzenko, SM, Selfinteracting vector-tensor multiplet, Phys. Lett., B 420, 64, (1998)
[13] Claus, P.; etal., Vector tensor multiplets, Fortsch. Phys., 47, 125, (1999)
[14] Gates, SJ; etal., An extended detailed investigation of first and second order supersymmetries for off-shell \( \mathcal{N} \) = 2 and \( \mathcal{N} \) = 4 supermultiplets, Symmetry, 7, 1080, (2015) · Zbl 1373.81352
[15] Gates, SJ; Stiffler, K., Adinkra ‘color’ confinement in exemplary off-shell constructions of 4D, \( \mathcal{N} \) = 2 supersymmetry representations, JHEP, 07, 051, (2014)
[16] Wess, J., Fermi-Bose supersymmetry, Lect. Notes Phys., 37, 352, (1975)
[17] Fayet, P., Fermi-Bose hypersymmetry, Nucl. Phys., B 113, 135, (1976)
[18] Gates, SJ; Rana, L., A theory of spinning particles for large N extended supersymmetry, Phys. Lett., B 352, 50, (1995)
[19] 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].
[20] Faux, M.; Gates, SJ, Adinkras: a graphical technology for supersymmetric representation theory, Phys. Rev., D 71, (2005)
[21] Gates, SJ; etal., 4D, N = 1 supersymmetry genomics (I), JHEP, 12, 008, (2009)
[22] Gates, SJ; etal., 4D, N = 1 supersymmetry genomics (II), JHEP, 06, 071, (2012) · Zbl 1398.81241
[23] Gates, SJ; Hallett, J.; Hubsch, T.; Stiffler, K., The real anatomy of complex linear superfields, Int. J. Mod. Phys., A 27, 1250143, (2012) · Zbl 1260.81224
[24] Chappell, I.; etal., 4D, N = 1 supergravity genomics, JHEP, 10, 004, (2013) · Zbl 1342.83460
[25] Gates, SJ; Hübsch, T.; Stiffler, K., Adinkras and SUSY Holography: Some explicit examples, Int. J. Mod. Phys., A 29, 1450041, (2014) · Zbl 1284.81143
[26] Gates, SJ; Hübsch, T.; Stiffler, K., On Clifford-algebraic dimensional extension and SUSY holography, Int. J. Mod. Phys., A 30, 1550042, (2015) · Zbl 1314.81096
[27] Calkins, M.; Gates, DEA; Gates, SJ; Stiffler, K., Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence, Int. J. Mod. Phys., A 30, 1550050, (2015) · Zbl 1321.81028
[28] Gates, SJ; etal., A Lorentz covariant holoraumy-induced “gadget” from minimal off-shell 4D, \( \mathcal{N} \) = 1 supermultiplets, JHEP, 11, 113, (2015) · Zbl 1388.81978
[29] Gates, DEA; Gates, SJ; Stiffler, K., A proposal on culling & filtering a coxeter group for 4D, \( \mathcal{N} \) = 1 spacetime SUSY representations: revised, JHEP, 08, 076, (2016) · Zbl 1390.81212
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.