Abstract
We initiate a systematic analysis of the nonrelativistic membrane solutions of M theory using the notion of 11d membrane Newton-Cartan (MNC) geometry as well as considering a 1/c2 expansion for the embedding fields of the M2 brane world-volume theory. We discuss the associated boost and dilatation symmetries of the nonrelativistic world-volume theory at leading order in the 1/c expansion. We show that, in the static gauge, when the world-volume directions of the nonrelativistic M2 brane are stretched along the longitudinal axes of the target space geometry, the leading order action in the 1/c expansion becomes trivial. In other words, the nontrivial dynamics appears to be only at NLO and beyond. In our analysis, we focus on such embeddings only and obtain the corresponding dispersion relation associated with the nonrelativistic world-volume theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys. 42 (2001) 3127 [hep-th/0009181] [INSPIRE].
U.H. Danielsson, A. Guijosa and M. Kruczenski, IIA/B, wound and wrapped, JHEP 10 (2000) 020 [hep-th/0009182] [INSPIRE].
J. Gomis, J. Gomis and K. Kamimura, Non-relativistic superstrings: A new soluble sector of AdS5 × S5, JHEP 12 (2005) 024 [hep-th/0507036] [INSPIRE].
E. Bergshoeff, J. Rosseel and T. Zojer, Newton-Cartan (super)gravity as a non-relativistic limit, Class. Quant. Grav. 32 (2015) 205003 [arXiv:1505.02095] [INSPIRE].
E.A. Bergshoeff, J. Lahnsteiner, L. Romano, J. Rosseel and C. Şimşek, A non-relativistic limit of NS-NS gravity, JHEP 06 (2021) 021 [arXiv:2102.06974] [INSPIRE].
D. Hansen, J. Hartong and N.A. Obers, Action Principle for Newtonian Gravity, Phys. Rev. Lett. 122 (2019) 061106 [arXiv:1807.04765] [INSPIRE].
E.A. Bergshoeff, J. Gomis, J. Rosseel, C. Şimşek and Z. Yan, String Theory and String Newton-Cartan Geometry, J. Phys. A 53 (2020) 014001 [arXiv:1907.10668] [INSPIRE].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-duality, JHEP 11 (2018) 133 [arXiv:1806.06071] [INSPIRE].
T. Harmark, J. Hartong and N.A. Obers, Nonrelativistic strings and limits of the AdS/CFT correspondence, Phys. Rev. D 96 (2017) 086019 [arXiv:1705.03535] [INSPIRE].
T. Harmark, J. Hartong, L. Menculini, N.A. Obers and Z. Yan, Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence, JHEP 11 (2018) 190 [arXiv:1810.05560] [INSPIRE].
D. Roychowdhury, Semiclassical dynamics for torsional Newton-Cartan strings, Nucl. Phys. B 958 (2020) 115132 [arXiv:1911.10473] [INSPIRE].
D. Roychowdhury, Nonrelativistic pulsating strings, JHEP 09 (2019) 002 [arXiv:1907.00584] [INSPIRE].
Z. Yan and M. Yu, KLT factorization of nonrelativistic string amplitudes, JHEP 04 (2022) 068 [arXiv:2112.00025] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, Nonrelativistic Open String and Yang-Mills Theory, JHEP 03 (2021) 269 [arXiv:2007.01886] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, T-duality in Nonrelativistic Open String Theory, JHEP 02 (2021) 087 [arXiv:2008.05493] [INSPIRE].
J. Hartong and E. Have, Nonrelativistic Expansion of Closed Bosonic Strings, Phys. Rev. Lett. 128 (2022) 021602 [arXiv:2107.00023] [INSPIRE].
T. Harmark, J. Hartong, L. Menculini, N.A. Obers and G. Oling, Relating non-relativistic string theories, JHEP 11 (2019) 071 [arXiv:1907.01663] [INSPIRE].
A.D. Gallegos, U. Gürsoy and N. Zinnato, Torsional Newton Cartan gravity from non-relativistic strings, JHEP 09 (2020) 172 [arXiv:1906.01607] [INSPIRE].
J. Gomis, J. Oh and Z. Yan, Nonrelativistic String Theory in Background Fields, JHEP 10 (2019) 101 [arXiv:1905.07315] [INSPIRE].
L. Bidussi, T. Harmark, J. Hartong, N.A. Obers and G. Oling, Torsional string Newton-Cartan geometry for non-relativistic strings, JHEP 02 (2022) 116 [arXiv:2107.00642] [INSPIRE].
Z. Yan, Torsional deformation of nonrelativistic string theory, JHEP 09 (2021) 035 [arXiv:2106.10021] [INSPIRE].
D. Roychowdhury, Probing tachyon kinks in Newton-Cartan background, Phys. Lett. B 795 (2019) 225 [arXiv:1903.05890] [INSPIRE].
K. Kamimura and T. Ramirez, Brane dualities in non-relativistic limit, JHEP 03 (2006) 058 [hep-th/0512146] [INSPIRE].
S. Ebert, H.-Y. Sun and Z. Yan, Dual D-brane actions in nonrelativistic string theory, JHEP 04 (2022) 161 [arXiv:2112.09316] [INSPIRE].
C.D.A. Blair, D. Gallegos and N. Zinnato, A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry, JHEP 10 (2021) 015 [arXiv:2104.07579] [INSPIRE].
E. Bergshoeff, J. Lahnsteiner, L. Romano and J. Rosseel, The supersymmetric Neveu-Schwarz branes of non-relativistic string theory, JHEP 08 (2022) 218 [arXiv:2204.04089] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. 660 (2003) 403] [hep-th/0205131] [INSPIRE].
J. Brugues, J. Rojo and J.G. Russo, Non-perturbative states in type-II superstring theory from classical spinning membranes, Nucl. Phys. B 710 (2005) 117 [hep-th/0408174] [INSPIRE].
M. Alishahiha and M. Ghasemkhani, Orbiting membranes in M-theory on AdS7 × S4 background, JHEP 08 (2002) 046 [hep-th/0206237] [INSPIRE].
M. Alishahiha and A.E. Mosaffa, Circular semiclassical string solutions on confining AdS/CFT backgrounds, JHEP 10 (2002) 060 [hep-th/0210122] [INSPIRE].
P. Bozhilov, M2-brane solutions in AdS7 × S4, JHEP 10 (2003) 032 [hep-th/0309215] [INSPIRE].
P. Bozhilov, Membrane solutions in M-theory, JHEP 08 (2005) 087 [hep-th/0507149] [INSPIRE].
J.A. Garcia, A. Guijosa and J.D. Vergara, A membrane action for OM theory, Nucl. Phys. B 630 (2002) 178 [hep-th/0201140] [INSPIRE].
M.P. Garcia Del Moral, C. Las Heras, P. Leon, J.M. Pena and A. Restuccia, M2-branes on a constant flux background, Phys. Lett. B 797 (2019) 134924 [arXiv:1811.11231] [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: 2208.05646
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
Roychowdhury, D. Nonrelativistic expansion of M2 branes and M theory backgrounds. J. High Energ. Phys. 2022, 152 (2022). https://doi.org/10.1007/JHEP11(2022)152
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)152