Abstract
Non-conformal supercurrents in six dimensions are described, which contain the trace of the energy-momentum tensor and the gamma-trace of the supersymmetry current amongst their component fields. Within the superconformal approach to \( \mathcal{N}=\left(1,\ 0\right) \) supergravity, we present various distinct non-conformal supercurrents, one of which is associated with an \( \mathcal{O}(2) \) (or linear) multiplet compensator, while another with a tensor multiplet compensator. We also derive an infinite class of non-conformal supercurrents involving \( \mathcal{O}(n) \) multiplets with n > 2. As an illustrative example we construct the relaxed hypermultiplet in supergravity. Finally, we put forward a non-conformal supercurrent in the \( \mathcal{N}=\left(2,0\right) \) supersymmetric case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Ferrara and B. Zumino, Transformation Properties of the Supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].
Y. Korovin, S.M. Kuzenko and S. Theisen, The conformal supercurrents in diverse dimensions and conserved superconformal currents, JHEP 05 (2016) 134 [arXiv:1604.00488] [INSPIRE].
P.S. Howe and U. Lindström, The Supercurrent in Five-dimensions, Phys. Lett. B 103 (1981) 422 [INSPIRE].
P.S. Howe, G. Sierra and P.K. Townsend, Supersymmetry in Six-Dimensions, Nucl. Phys. B 221 (1983) 331 [INSPIRE].
S.J. Gates Jr., Super p-form gauge superfields, Nucl. Phys. B 184 (1981) 381 [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
T.E. Clark, O. Piguet and K. Sibold, Supercurrents, Renormalization and Anomalies, Nucl. Phys. B 143 (1978) 445 [INSPIRE].
M.F. Sohnius and P.C. West, An Alternative Minimal Off-Shell Version of N = 1 Supergravity, Phys. Lett. B 105 (1981) 353 [INSPIRE].
S.J. Gates Jr., M.T. Grisaru and W. Siegel, Auxiliary field anomalies, Nucl. Phys. B 203 (1982) 189 [INSPIRE].
V. Ogievetsky and E. Sokatchev, On Vector Superfield Generated by Supercurrent, Nucl. Phys. B 124 (1977) 309 [INSPIRE].
S. Ferrara and B. Zumino, Structure of Conformal Supergravity, Nucl. Phys. B 134 (1978) 301 [INSPIRE].
W. Siegel, A derivation of the supercurrent superfield, Harvard preprint HUTP-77/A089 (1977).
J. Wess and B. Zumino, Superfield Lagrangian for Supergravity, Phys. Lett. B 74 (1978) 51 [INSPIRE].
K.S. Stelle and P.C. West, Minimal Auxiliary Fields for Supergravity, Phys. Lett. B 74 (1978) 330 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, The Auxiliary Fields of Supergravity, Phys. Lett. B 74 (1978) 333 [INSPIRE].
S. Deser, Scale invariance and gravitational coupling, Annals Phys. 59 (1970) 248 [INSPIRE].
B. Zumino, Effective Lagrangians and broken symmetries, in Lectures on Elementary Particles and Quantum Field Theory. Vol. 2, S. Deser, M. Grisaru and H. Pendleton eds., the M.I.T. Press, Cambridge U.S.A. (1970), pp. 437-500.
P.A.M. Dirac, Long range forces and broken symmetries, Proc. Roy. Soc. Lond. A 333 (1973) 403 [INSPIRE].
W. Siegel, A polynomial action for a massive, self-interacting chiral superfield coupled to supergravity, HUTP-77/A077 (1977).
M. Kaku and P.K. Townsend, Poincaré supergravity as broken superconformal gravity, Phys. Lett. B 76 (1978) 54 [INSPIRE].
R. Manvelyan and W. Rühl, On the supermultiplet of anomalous currents in D = 6, Phys. Lett. B 567 (2003) 53 [hep-th/0305138] [INSPIRE].
K.S. Stelle, Extended supercurrents and the ultraviolet finiteness of N=4 supersymmetric Yang-Mills theory, in Quantum Structure of Space and Time, M.J. Duff and C.J. Isham eds., Cambridge University Press, Cambridge (1982), pp. 337-361.
M.F. Sohnius, The Multiplet of Currents for N = 2 Extended Supersymmetry, Phys. Lett. B 81 (1979) 8 [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, Supercurrents, Nucl. Phys. B 192 (1981) 332 [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].
D. Butter and S.M. Kuzenko, N=2 supergravity and supercurrents, JHEP 12 (2010) 080 [arXiv:1011.0339] [INSPIRE].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E. Sokatchev, N = 2 Supergravity in Superspace: Different Versions and Matter Couplings, Class. Quant. Grav. 4 (1987) 1255 [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge (2001).
S.V. Ketov and B.B. Lokhvitsky, Some Generalizations of N = 2 Yang-Mills Matter Couplings, Class. Quant. Grav. 4 (1987) L137 [INSPIRE].
S.V. Ketov, B.B. Lokhvitsky and I.V. Tyutin, HyperKähler σ Models in Extended Superspace, Theor. Math. Phys. 71 (1987) 496 [Teor. Mat. Fiz. 71 (1987) 226] [INSPIRE].
A.S. Galperin, E.A. Ivanov and V.I. Ogievetsky, Duality Transformations and Most General Matter Selfcoupling in N = 2 Supersymmetry, Nucl. Phys. B 282 (1987) 74 [INSPIRE].
U. Lindström and M. Roček, New HyperKähler Metrics and New Supermultiplets, Commun. Math. Phys. 115 (1988) 21 [INSPIRE].
M.F. Sohnius, K.S. Stelle and P.C. West, Representations of extended supersymmetry, in Superspace and Supergravity, S.W. Hawking and M. Roček eds., Cambridge University Press, Cambridge (1981), p. 283-329.
F. Gonzalez-Rey, M. Roček, S. Wiles, U. Lindström and R. von Unge, Feynman rules in N = 2 projective superspace: 1. Massless hypermultiplets, Nucl. Phys. B 516 (1998) 426 [hep-th/9710250] [INSPIRE].
W.D. Linch, III and G. Tartaglino-Mazzucchelli, Six-dimensional Supergravity and Projective Superfields, JHEP 08 (2012) 075 [arXiv:1204.4195] [INSPIRE].
S.M. Kuzenko, On compactified harmonic/projective superspace, 5-D superconformal theories and all that, Nucl. Phys. B 745 (2006) 176 [hep-th/0601177] [INSPIRE].
S.M. Kuzenko, On superconformal projective hypermultiplets, JHEP 12 (2007) 010 [arXiv:0710.1479] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Super-Weyl invariance in 5D supergravity, JHEP 04 (2008) 032 [arXiv:0802.3953] [INSPIRE].
S.M. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, On conformal supergravity and projective superspace, JHEP 08 (2009) 023 [arXiv:0905.0063] [INSPIRE].
D. Butter, S.M. Kuzenko, J. Novak and S. Theisen, Invariants for minimal conformal supergravity in six dimensions, JHEP 12 (2016) 072 [arXiv:1606.02921] [INSPIRE].
S.M. Kuzenko, J. Novak and I.B. Samsonov, The anomalous current multiplet in 6D minimal supersymmetry, JHEP 02 (2016) 132 [arXiv:1511.06582] [INSPIRE].
S.M. Kuzenko, J. Novak and I.B. Samsonov, Chiral anomalies in six dimensions from harmonic superspace, JHEP 11 (2017) 145 [arXiv:1708.08238] [INSPIRE].
E.A. Ivanov, A.V. Smilga and B.M. Zupnik, Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B 726 (2005) 131 [hep-th/0505082] [INSPIRE].
J. Grundberg and U. Lindström, Actions for Linear Multiplets in Six-dimensions, Class. Quant. Grav. 2 (1985) L33 [INSPIRE].
E. Bergshoeff, E. Sezgin and A. Van Proeyen, Superconformal Tensor Calculus and Matter Couplings in Six-dimensions, Nucl. Phys. B 264 (1986) 653 [Erratum ibid. B 598 (2001) 667] [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, The Relaxed Hypermultiplet: An Unconstrained N = 2 Superfield Theory, Nucl. Phys. B 214 (1983) 519 [INSPIRE].
C. Arias, W.D. Linch, III and A.K. Ridgway, Superforms in six-dimensional superspace, JHEP 05 (2016) 016 [arXiv:1402.4823] [INSPIRE].
S.M. Kuzenko, J. Novak and S. Theisen, New superconformal multiplets and higher derivative invariants in six dimensions, Nucl. Phys. B 925 (2017) 348 [arXiv:1707.04445] [INSPIRE].
E. Sokatchev, Off-shell Six-dimensional Supergravity in Harmonic Superspace, Class. Quant. Grav. 5 (1988) 1459 [INSPIRE].
P.S. Howe and A. Umerski, Anomaly multiplets in six-dimensions and ten-dimensions, Phys. Lett. B 198 (1987) 57 [INSPIRE].
F. Coomans and A. Van Proeyen, Off-shell N=(1,0), D = 6 supergravity from superconformal methods, JHEP 02 (2011) 049 [Erratum ibid. 01 (2012) 119] [arXiv:1101.2403] [INSPIRE].
D. Butter, J. Novak and G. Tartaglino-Mazzucchelli, The component structure of conformal supergravity invariants in six dimensions, JHEP 05 (2017) 133 [arXiv:1701.08163] [INSPIRE].
E. Bergshoeff, F. Coomans, E. Sezgin and A. Van Proeyen, Higher Derivative Extension of 6D Chiral Gauged Supergravity, JHEP 07 (2012) 011 [arXiv:1203.2975] [INSPIRE].
L. Bonora, P. Pasti and M. Tonin, Cohomologies and Anomalies in Supersymmetric Theories, Nucl. Phys. B 252 (1985) 458 [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Matter Superfields in External Supergravity: Green Functions, Effective Action and Superconformal Anomalies, Nucl. Phys. B 274 (1986) 653 [INSPIRE].
S.M. Kuzenko, Super-Weyl anomalies in N = 2 supergravity and (non)local effective actions, JHEP 10 (2013) 151 [arXiv:1307.7586] [INSPIRE].
A. Karlhede, U. Lindström and M. Roček, Selfinteracting Tensor Multiplets in N = 2 Superspace, Phys. Lett. B 147 (1984) 297 [INSPIRE].
U. Lindström and M. Roček, N = 2 Super Yang-Mills Theory in Projective Superspace, Commun. Math. Phys. 128 (1990) 191 [INSPIRE].
S.M. Kuzenko and W.D. Linch, III, On five-dimensional superspaces, JHEP 02 (2006) 038 [hep-th/0507176] [INSPIRE].
S.J. Gates Jr., S. Penati and G. Tartaglino-Mazzucchelli, 6D supersymmetry, projective superspace and 4D, N = 1 superfields, JHEP 05 (2006) 051 [hep-th/0508187] [INSPIRE].
S.J. Gates Jr., S. Penati and G. Tartaglino-Mazzucchelli, 6D Supersymmetric Nonlinear σ-models in 4D, N = 1 Superspace, JHEP 09 (2006) 006 [hep-th/0604042] [INSPIRE].
D. Butter, S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Conformal supergravity in five dimensions: New approach and applications, JHEP 02 (2015) 111 [arXiv:1410.8682] [INSPIRE].
D. Butter, New approach to curved projective superspace, Phys. Rev. D 92 (2015) 085004 [arXiv:1406.6235] [INSPIRE].
D. Butter, Projective multiplets and hyperkähler cones in conformal supergravity, JHEP 06 (2015) 161 [arXiv:1410.3604] [INSPIRE].
E. Bergshoeff, E. Sezgin and E. Sokatchev, Couplings of selfdual tensor multiplet in six-dimensions, Class. Quant. Grav. 13 (1996) 2875 [hep-th/9605087] [INSPIRE].
C. Grojean and J. Mourad, Superconformal 6-D (2, 0) theories in superspace, Class. Quant. Grav. 15 (1998) 3397 [hep-th/9807055] [INSPIRE].
P. Arvidsson, E. Flink and M. Henningson, Supersymmetric coupling of a selfdual string to a (2,0) tensor multiplet background, JHEP 11 (2003) 015 [hep-th/0309244] [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: 1709.09892
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Kuzenko, S.M., Novak, J. & Theisen, S. Non-conformal supercurrents in six dimensions. J. High Energ. Phys. 2018, 30 (2018). https://doi.org/10.1007/JHEP02(2018)030
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)030