Abstract
For all types of \( \mathcal{N} \) = 4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The \( \mathcal{N} \) = 4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only \( \mathcal{N} \) = 2 supersymmetry is manifest. Using the off-shell structure of the \( \mathcal{N} \) = 4 vector multiplets, we provide complete \( \mathcal{N} \) = 4 SYM actions in (2,0) AdS superspace for all types of \( \mathcal{N} \) = 4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting \( \mathcal{N} \) = 2 action contains a Chern-Simons term proportional to q/r, where r is the radius of AdS 3 and q is the R-charge of a chiral scalar superfield. The R-charge is a linear inhomogeneous function of X, an expectation value of the \( \mathcal{N} \) = 4 Cotton superfield. Thus our results explain the mysterious structure of \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theories on S 3 discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no Chern-Simons and chiral mass-like terms.
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References
I.B. Samsonov and D. Sorokin, Superfield theories on S 3 and their localization, arXiv:1401.7952 [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Three-dimensional (p,q) AdS superspaces and matter couplings, JHEP 08 (2012) 024 [arXiv:1205.4622] [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons Action for Three-Dimensional anti-de Sitter Supergravity Theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
P.S. Howe, J.M. Izquierdo, G. Papadopoulos and P.K. Townsend, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys. B 467 (1996) 183 [hep-th/9505032] [INSPIRE].
S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Off-shell supergravity-matter couplings in three dimensions, JHEP 03 (2011) 120 [arXiv:1101.4013] [INSPIRE].
D. Butter, S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Nonlinear σ-models with AdS supersymmetry in three dimensions, JHEP 02 (2013) 121 [arXiv:1210.5906] [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, New HyperKähler Metrics and New Supermultiplets, Commun. Math. Phys. 115 (1988) 21 [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 G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 (AdS) supergravity and associated supercurrents, JHEP 12 (2011) 052 [arXiv:1109.0496] [INSPIRE].
B. DeWitt, Supermanifolds, Cambridge University Press, Cambridge, U.K. (1992).
I.A. Bandos, E. Ivanov, J. Lukierski and D. Sorokin, On the superconformal flatness of AdS superspaces, JHEP 06 (2002) 040 [hep-th/0205104] [INSPIRE].
R. Brooks and S.J. Gates Jr., Extended supersymmetry and superBF gauge theories, Nucl. Phys. B 432 (1994) 205 [hep-th/9407147] [INSPIRE].
B. Zupnik, Harmonic superpotentials and symmetries in gauge theories with eight supercharges, Nucl. Phys. B 554 (1999) 365 [Erratum ibid. B 644 (2002) 405] [hep-th/9902038] [INSPIRE].
S.M. Kuzenko and J. Novak, Supergravity-matter actions in three dimensions and Chern-Simons terms, arXiv:1401.2307 [INSPIRE].
W. Siegel, Chiral Actions for N = 2 Supersymmetric Tensor Multiplets, Phys. Lett. B 153 (1985) 51 [INSPIRE].
F. Gonzalez-Rey, Feynman rules in N = 2 projective superspace. 3. Yang-Mills multiplet, hep-th/9712128 [INSPIRE].
S.M. Kuzenko, Projective superspace as a double punctured harmonic superspace, Int. J. Mod. Phys. A 14 (1999) 1737 [hep-th/9806147] [INSPIRE].
S.M. Kuzenko, On N = 2 supergravity and projective superspace: Dual formulations, Nucl. Phys. B 810 (2009) 135 [arXiv:0807.3381] [INSPIRE].
S.M. Kuzenko, Five-dimensional supersymmetric Chern-Simons action as a hypermultiplet quantum correction, Phys. Lett. B 644 (2007) 88 [hep-th/0609078] [INSPIRE].
S.J. Gates Jr., 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].
B.M. Zupnik, The Action of the Supersymmetric N = 2 Gauge Theory in Harmonic Superspace, Phys. Lett. B 183 (1987) 175 [INSPIRE].
N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček, HyperKähler Metrics and Supersymmetry, Commun. Math. Phys. 108 (1987) 535 [INSPIRE].
B.M. Zupnik and D.G. Pak, Superfield Formulation of the Simplest Three-dimensional Gauge Theories and Conformal Supergravities, Theor. Math. Phys. 77 (1988) 1070 [Teor. Mat. Fiz. 77 (1988) 97] [INSPIRE].
E.A. Ivanov, Chern-Simons matter systems with manifest N = 2 supersymmetry, Phys. Lett. B 268 (1991) 203 [INSPIRE].
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Kuzenko, S.M., Tartaglino-Mazzucchelli, G. \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theories in AdS3 . J. High Energ. Phys. 2014, 18 (2014). https://doi.org/10.1007/JHEP05(2014)018
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DOI: https://doi.org/10.1007/JHEP05(2014)018