Abstract
In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1…αk) of arbitrary rank in four-dimensional \( \mathcal{N} \) = 1 superconformal theory. We find that the correlation function of three such operators \( \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\beta \left(k+l\right)}\left({z}_2\right){\overline{S}}_{\dot{\gamma}(l)}\left({z}_3\right)\right\rangle \) is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l. In addition, we present the general structure of mixed correlators of the form \( \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right)L\left({z}_3\right)\right\rangle \) and \( \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right){J}_{\gamma \dot{\gamma}}\left({z}_3\right)\right\rangle \), where L is the flavour current multiplet and \( {J}_{\gamma \dot{\gamma}} \) is the supercurrent.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
J. Erdmenger and H. Osborn, Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [INSPIRE].
A.M. Polyakov, Conformal symmetry of critical fluctuations, JETP Lett. 12 (1970) 381 [Pisma Zh. Eksp. Teor. Fiz. 12 (1970) 538] [INSPIRE].
E.J. Schreier, Conformal symmetry and three-point functions, Phys. Rev. D 3 (1971) 980 [INSPIRE].
A.A. Migdal, On hadronic interactions at small distances, Phys. Lett. B 37 (1971) 98 [INSPIRE].
A.A. Migdal, Conformal invariance and bootstrap, Phys. Lett. B 37 (1971) 386 [INSPIRE].
S. Ferrara, A.F. Grillo and R. Gatto, Manifestly conformal-covariant expansion on the light cone, Phys. Rev. D 5 (1972) 3102 [INSPIRE].
S. Ferrara, A.F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161 [INSPIRE].
K. Koller, The significance of conformal inversion in quantum field theory, Commun. Math. Phys. 40 (1974) 15 [DESY-74-8].
G. Mack, Convergence of operator product expansions on the vacuum in conformal invariant quantum field theory, Commun. Math. Phys. 53 (1977) 155.
Y.S. Stanev, Stress-energy tensor and U(1) current operator product expansions in conformal QFT, Bulg. J. Phys. 15 (1988) 93.
E.S. Fradkin and M.Y. Palchik, Recent developments in conformal invariant quantum field theory, Phys. Rept. 44 (1978) 249 [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A note on CFT correlators in three dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [INSPIRE].
J.-H. Park, N = 1 superconformal symmetry in four-dimensions, Int. J. Mod. Phys. A 13 (1998) 1743 [hep-th/9703191] [INSPIRE].
H. Osborn, N = 1 superconformal symmetry in four-dimensional quantum field theory, Annals Phys. 272 (1999) 243 [hep-th/9808041] [INSPIRE].
J.-H. Park, Superconformal symmetry and correlation functions, Nucl. Phys. B 559 (1999) 455 [hep-th/9903230] [INSPIRE].
J.-H. Park, Superconformal symmetry in six-dimensions and its reduction to four-dimensions, Nucl. Phys. B 539 (1999) 599 [hep-th/9807186] [INSPIRE].
J.-H. Park, Superconformal symmetry in three-dimensions, J. Math. Phys. 41 (2000) 7129 [hep-th/9910199] [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].
A.A. Nizami, T. Sharma and V. Umesh, Superspace formulation and correlation functions of 3d superconformal field theories, JHEP 07 (2014) 022 [arXiv:1308.4778] [INSPIRE].
E.I. Buchbinder, S.M. Kuzenko and I.B. Samsonov, Superconformal field theory in three dimensions: correlation functions of conserved currents, JHEP 06 (2015) 138 [arXiv:1503.04961] [INSPIRE].
E.I. Buchbinder, S.M. Kuzenko and I.B. Samsonov, Implications of \( \mathcal{N} \) = 4 superconformal symmetry in three spacetime dimensions, JHEP 08 (2015) 125 [arXiv:1507.00221] [INSPIRE].
S.M. Kuzenko and I.B. Samsonov, Implications of \( \mathcal{N} \) = 5, 6 superconformal symmetry in three spacetime dimensions, JHEP 08 (2016) 084 [arXiv:1605.08208] [INSPIRE].
E.I. Buchbinder and B.J. Stone, Mixed three-point functions of conserved currents in three-dimensional superconformal field theory, Phys. Rev. D 103 (2021) 086023 [arXiv:2102.04827] [INSPIRE].
S. Ferrara and B. Zumino, Transformation properties of the supercurrent, Nucl. Phys. B 87 (1975) 207.
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Frontiers in Physics volume 58, Benjamin/Cummings, Reading U.S.A. (1983) [hep-th/0108200] [INSPIRE].
M. Magro, I. Sachs and S. Wolf, Superfield Noether procedure, Annals Phys. 298 (2002) 123 [hep-th/0110131] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
S.M. Kuzenko, Variant supercurrent multiplets, JHEP 04 (2010) 022 [arXiv:1002.4932] [INSPIRE].
S.M. Kuzenko, Variant supercurrents and Noether procedure, Eur. Phys. J. C 71 (2011) 1513 [arXiv:1008.1877] [INSPIRE].
S. Ferrara, J. Wess and B. Zumino, Supergauge multiplets and superfields, Phys. Lett. B 51 (1974) 239.
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
Y.S. Stanev, Constraining conformal field theory with higher spin symmetry in four dimensions, Nucl. Phys. B 876 (2013) 651 [arXiv:1307.5209] [INSPIRE].
V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in d = 4, arXiv:1307.8092 [INSPIRE].
V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions, JHEP 03 (2016) 044 [arXiv:1510.02535] [INSPIRE].
S.R. Coleman and J. Mandula, All possible symmetries of the S matrix, Phys. Rev. 159 (1967) 1251 [INSPIRE].
Y.S. Stanev, Correlation functions of conserved currents in four dimensional conformal field theory, Nucl. Phys. B 865 (2012) 200 [arXiv:1206.5639] [INSPIRE].
A. Zhiboedov, A note on three-point functions of conserved currents, arXiv:1206.6370 [INSPIRE].
E. Elkhidir, D. Karateev and M. Serone, General three-point functions in 4D CFT, JHEP 01 (2015) 133 [arXiv:1412.1796] [INSPIRE].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS5 × T11: Predictions on N = 1 SCFT’s, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [INSPIRE].
S.M. Kuzenko and E.S.N. Raptakis, Symmetries of supergravity backgrounds and supersymmetric field theory, JHEP 04 (2020) 133 [arXiv:1912.08552] [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, Supercurrents, Nucl. Phys. B 192 (1981) 332 [INSPIRE].
M.F. Sohnius, The multiplet of currents for N = 2 extended supersymmetry, Phys. Lett. B 81 (1979) 8 [INSPIRE].
S.M. Kuzenko, R. Manvelyan and S. Theisen, Off-shell superconformal higher spin multiplets in four dimensions, JHEP 07 (2017) 034 [arXiv:1701.00682] [INSPIRE].
E.I. Buchbinder, J. Hutomo and S.M. Kuzenko, Higher spin supercurrents in Anti-de Sitter space, JHEP 09 (2018) 027 [arXiv:1805.08055] [INSPIRE].
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions, JHEP 08 (2018) 055 [arXiv:1805.04413] [INSPIRE].
S.J. Gates and K. Koutrolikos, Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents, Phys. Lett. B 797 (2019) 134868 [arXiv:1904.13336] [INSPIRE].
S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett. 57 (1993) 534 [Pisma Zh. Eksp. Teor. Fiz. 57 (1993) 521] [INSPIRE].
S.M. Kuzenko and A.G. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett. 57 (1993) 539 [Pisma Zh. Eksp. Teor. Fiz. 57 (1993) 526] [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity or a walk through superspace, IOP, Bristol, U.K. (1995), revised edition (1998).
E.I. Buchbinder, J. Hutomo and S.M. Kuzenko, Correlation functions of spinor current multiplets in \( \mathcal{N} \) = 1 superconformal theory, JHEP 07 (2021) 165 [arXiv:2103.09472] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2106.14498
Rights and permissions
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.
About this article
Cite this article
Buchbinder, E.I., Hutomo, J. & Kuzenko, S.M. Three-point functions of higher-spin spinor current multiplets in \( \mathcal{N} \) = 1 superconformal theory. J. High Energ. Phys. 2021, 58 (2021). https://doi.org/10.1007/JHEP10(2021)058
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2021)058