Abstract
Nonrelativistic string theory in flat spacetime is described by a two-dimensional quantum field theory with a nonrelativistic global symmetry acting on the worldsheet fields. Nonrelativistic string theory is unitary, ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying nonrelativistic symmetry. The worldsheet theory of nonrelativistic string theory is coupled to a curved spacetime background and to a Kalb-Ramond two-form and dilaton field. The appropriate spacetime geometry for nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is distinct from Riemannian geometry. This defines the sigma model of nonrelativistic string theory describing strings propagating and interacting in curved background fields. We also implement T-duality transformations in the path integral of this sigma model and uncover the spacetime interpretation of T-duality. We show that T-duality along the longitudinal direction of the string Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This relation provides a first principles definition of string theory in the discrete light cone quantization (DLCQ) in an arbitrary background, a quantization that appears in nonperturbative approaches to quantum field theory and string/M-theory, such as in Matrix theory. T-duality along a transverse direction of the string Newton-Cartan geometry equates nonrelativistic string theory in two distinct, T-dual backgrounds.
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References
J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys. 42 (2001) 3127 [hep-th/0009181] [INSPIRE].
I.R. Klebanov and J.M. Maldacena, (1+1)-dimensional NCOS and its U(N) gauge theory dual, Int. J. Mod. Phys. A 16 (2001) 922 [hep-th/0006085] [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 AdS 5 × S 5, JHEP 12 (2005) 024 [hep-th/0507036] [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. Bergshoeff, J. Gomis, J. Rosseel, C. Şimsek and Z. Yan, in preparation, (2018).
C. Batlle, J. Gomis and D. Not, Extended Galilean symmetries of non-relativistic strings, JHEP 02 (2017) 049 [arXiv:1611.00026] [INSPIRE].
J. Gomis and P.K. Townsend, The Galilean superstring, JHEP 02 (2017) 105 [arXiv:1612.02759] [INSPIRE].
C. Batlle, J. Gomis, L. Mezincescu and P.K. Townsend, Tachyons in the Galilean limit, JHEP 04 (2017) 120 [arXiv:1702.04792] [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].
J. Klusoň, Remark about non-relativistic string in Newton-Cartan background and null reduction, JHEP 05 (2018) 041 [arXiv:1803.07336] [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
L. Susskind, Another conjecture about M(atrix) theory, hep-th/9704080 [INSPIRE].
N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009] [INSPIRE].
A. Sen, D0-branes on T n and matrix theory, Adv. Theor. Math. Phys. 2 (1998) 51 [hep-th/9709220] [INSPIRE].
S. Hellerman and J. Polchinski, Compactification in the lightlike limit, Phys. Rev. D 59 (1999) 125002 [hep-th/9711037] [INSPIRE].
A. Bagchi and R. Gopakumar, Galilean conformal algebras and AdS/CFT, JHEP 07 (2009) 037 [arXiv:0902.1385] [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].
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].
D.H. Friedan, Nonlinear models in 2 + ϵ dimensions, Annals Phys. 163 (1985) 318 [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].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [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 [arXiv:1707.03713] [INSPIRE].
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Bergshoeff, E., Gomis, J. & Yan, Z. Nonrelativistic string theory and T-duality. J. High Energ. Phys. 2018, 133 (2018). https://doi.org/10.1007/JHEP11(2018)133
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DOI: https://doi.org/10.1007/JHEP11(2018)133