Abstract
Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first principles. In these notes, we focus on the bosonic closed string sector. In curved spacetime, nonrelativistic string theory is defined by a renormalizable quantum nonlinear sigma model in background fields, following certain symmetry principles that disallow any deformation towards relativistic string theory. We review previous proposals of such symmetry principles and propose a modified version that might be useful for supersymmetrizations. The appropriate target-space geometry determined by these local spacetime symmetries is string Newton-Cartan geometry. This geometry is equipped with a two-dimensional foliation structure that is restricted by torsional constraints. Breaking the symmetries that give rise to such torsional constraints in the target space will in general generate quantum corrections to a marginal deformation in the worldsheet quantum field theory. Such a deformation induces a renormalization group flow towards sigma models that describe relativistic strings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I.R. Klebanov and J.M. Maldacena, (1 + 1)-dimensional NCOS and its U(N) gauge theory dual, Adv. Theor. Math. Phys. 4 (2000) 283 [hep-th/0006085] [INSPIRE].
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].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-duality, JHEP 11 (2018) 133 [arXiv:1806.06071] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, T-duality in Nonrelativistic Open String Theory, JHEP 02 (2021) 087 [arXiv:2008.05493] [INSPIRE].
T. Banks and N. Seiberg, Strings from matrices, Nucl. Phys. B 497 (1997) 41 [hep-th/9702187] [INSPIRE].
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43 [hep-th/9703030] [INSPIRE].
L. Motl, Proposals on nonperturbative superstring interactions, hep-th/9701025 [INSPIRE].
J. Gomis, Z. Yan and M. Yu, Nonrelativistic Open String and Yang-Mills Theory, JHEP 03 (2021) 269 [arXiv:2007.01886] [INSPIRE].
U.H. Danielsson, A. Guijosa and M. Kruczenski, Newtonian gravitons and D-brane collective coordinates in wound string theory, JHEP 03 (2001) 041 [hep-th/0012183] [INSPIRE].
J. Gomis, J. Oh and Z. Yan, Nonrelativistic String Theory in Background Fields, JHEP 10 (2019) 101 [arXiv:1905.07315] [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].
A.D. Gallegos, U. Gürsoy and N. Zinnato, Torsional Newton Cartan gravity from non-relativistic strings, JHEP 09 (2020) 172 [arXiv:1906.01607] [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].
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].
R. Andringa, E. Bergshoeff, J. Gomis and M. de Roo, ‘Stringy’ Newton-Cartan Gravity, Class. Quant. Grav. 29 (2012) 235020 [arXiv:1206.5176] [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].
A.D. Gallegos, U. Gürsoy, S. Verma and N. Zinnato, Non-Riemannian gravity actions from double field theory, JHEP 06 (2021) 173 [arXiv:2012.07765] [INSPIRE].
Z. Yan and M. Yu, Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory, JHEP 03 (2020) 181 [arXiv:1912.03181] [INSPIRE].
L. Bidussi, T. Harmark, J. Hartong, N.A. Obers and G. Oling, Torsional string Newton-Cartan geometry for non-relativistic strings, arXiv:2107.00642 [INSPIRE].
C. Batlle, J. Gomis and D. Not, Extended Galilean symmetries of non-relativistic strings, JHEP 02 (2017) 049 [arXiv:1611.00026] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, KLT factorization and nonrelativistic string amplitudes, work in progress.
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press ((2007)), [DOI] [INSPIRE].
G. Grignani, M. Orselli and G.W. Semenoff, Matrix strings in a B field, JHEP 07 (2001) 004 [hep-th/0104112] [INSPIRE].
C.G. Callan Jr., E.J. Martinec, M.J. Perry and D. Friedan, Strings in Background Fields, Nucl. Phys. B 262 (1985) 593 [INSPIRE].
C.D.A. Blair, G. Oling and J.-H. Park, Non-Riemannian isometries from double field theory, JHEP 04 (2021) 072 [arXiv:2012.07766] [INSPIRE].
S.M. Ko, C. Melby-Thompson, R. Meyer and J.-H. Park, Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory, JHEP 12 (2015) 144 [arXiv:1508.01121] [INSPIRE].
K. Morand and J.-H. Park, Classification of non-Riemannian doubled-yet-gauged spacetime, Eur. Phys. J. C 77 (2017) 685 [Erratum ibid. 78 (2018) 901] [arXiv:1707.03713] [INSPIRE].
A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].
L. Freidel, R.G. Leigh and D. Minic, Metastring Theory and Modular Space-time, JHEP 06 (2015) 006 [arXiv:1502.08005] [INSPIRE].
J. Brugues, J. Gomis and K. Kamimura, Newton-Hooke algebras, non-relativistic branes and generalized pp-wave metrics, Phys. Rev. D 73 (2006) 085011 [hep-th/0603023] [INSPIRE].
J. Brugues, T. Curtright, J. Gomis and L. Mezincescu, Non-relativistic strings and branes as non-linear realizations of Galilei groups, Phys. Lett. B 594 (2004) 227 [hep-th/0404175] [INSPIRE].
E.A. Bergshoeff, K.T. Grosvenor, C. Simsek and Z. Yan, An Action for Extended String Newton-Cartan Gravity, JHEP 01 (2019) 178 [arXiv:1810.09387] [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: 2106.10021
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
Yan, Z. Torsional deformation of nonrelativistic string theory. J. High Energ. Phys. 2021, 35 (2021). https://doi.org/10.1007/JHEP09(2021)035
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2021)035