Abstract
We construct a superfield formulation for non-relativistic Chern–Simons-matter theories with manifest dynamical supersymmetry. By eliminating all the auxiliary fields, we show that the simple action reduces to the one obtained by taking non-relativistic limit from the relativistic Chern–Simons-matter theory proposed in the literature. As a further application, we give a manifestly supersymmetric derivation of the non-relativistic ABJM theory.
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Aharony O., Bergman O., Jafferis D.L., Maldacena J.: N = 6 superconformal Chern–Simons-matter theories, M2-branes and their gravity duals. JHEP 0810, 091 (2008) [arXiv:0806.1218 [hep-th]]
Balasubramanian, K., McGreevy, J.: Gravity duals for non-relativistic CFTs. arXiv:0804.4053 [hep-th]
Barut A.O., Xu B.W.: Conformal covariance and the probability interpretation of wave equations. Phys. Lett. A 82, 218 (1981)
de Azcarraga J.A., Ginestar D.: Nonrelativistic limit of supersymmetric theories. J. Math. Phys. 32, 3500 (1991)
Gates S.J., Grisaru M.T., Rocek M., Siegel W.: Superspace, or one thousand and one lessons in supersymmetry. Front. Phys. 58, 1 (1983) [arXiv:hep-th/0108200]
Gomis J., Rodriguez-Gomez D., Van Raamsdonk M., Verlinde H.: A massive study of M2-brane proposals. JHEP 0809, 113 (2008) [arXiv:0807.1074 [hep-th]]
Hagen C.R.: Scale and conformal transformations in galilean-covariant field theory. Phys. Rev. D 5, 377 (1972)
Horava, P.: Quantum criticality and Yang-Mills gauge theory. arXiv:0811.2217 [hep-th]
Hosomichi K., Lee K.M., Lee S., Lee S., Park J.: N = 5,6 superconformal Chern– Simons theories and M2-branes on orbifolds. JHEP 0809, 002 (2008) [arXiv:0806.4977 [hep-th]]
Jackiw R., Pi S.Y.: Classical and quantal nonrelativistic Chern–Simons theory. Phys. Rev. D 42, 3500 (1990) [Erratum-ibid. D 48, 3929 (1993)]
Jackiw, R., Pi, S.Y.: Finite and infinite symmetries in (2 + 1)-dimensional field theory. arXiv:hep-th/9206092
Leblanc M., Lozano G., Min H.: Extended superconformal Galilean symmetry in Chern-Simons matter systems. Ann. Phys. 219, 328 (1992) [arXiv:hep-th/9206039]
Nakayama Y.: Index for Non-relativistic Superconformal field theories. JHEP 0810, 083 (2008) [arXiv:0807.3344 [hep-th]]
Nakayama, Y., Sakaguchi, M., Yoshida, K.: Interacting SUSY-singlet matter in non-relativistic Chern–Simons theory. arXiv:0812.1564 [hep-th].
Nakayama, Y., Sakaguchi, M., Yoshida, K.: Non-Relativistic M2-brane gauge theory and new superconformal algebra. arXiv:0902.2204 [hep-th]
Nakayama Y., Ryu S., Sakaguchi M., Yoshida K.: A family of super Schrodinger invariant Chern-Simons matter systems. JHEP 0901, 006 (2009) [arXiv:0811.2461 [hep-th]]
Nicolai H.: Supersymmetry and spin systems. J. Phys. A 9, 1497 (1976)
Niederer U.: The maximal kinematical invariance group of the free Schrodinger equation. Helv. Phys. Acta 45, 802 (1972)
Perroud M.: Projective representations of the Schrodinger Group. Helv. Phys. Acta 50, 233 (1977)
Salam A., Strathdee J.A.: Supergauge transformations. Nucl. Phys. B 76, 477 (1974)
Son, D.T.: Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry. arXiv:0804.3972 [hep-th]
Wess J., Bagger J.: Supersymmetry and supergravity, p. 259. Princeton University Press, Princeton (1992)
Acknowledgements
The author would like to thank M. Sakaguchi, C. M. Thompson and K. Yoshida for fruitful discussions. The work was supported in part by the National Science Foundation under Grant No. PHY05-55662 and the UC Berkeley Center for Theoretical Physics.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nakayama, Y. Superfield Formulation for Non-Relativistic Chern–Simons-Matter Theory. Lett Math Phys 89, 67–83 (2009). https://doi.org/10.1007/s11005-009-0327-2
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DOI: https://doi.org/10.1007/s11005-009-0327-2