Abstract
The classical and quantum worldsheet theory describing nonrelativistic open string theory in an arbitrary nonrelativistic open and closed string background is constructed. We show that the low energy dynamics of open strings ending on n coincident D-branes in flat spacetime is described by a Galilean invariant U(n) Yang-Mills theory. We also study nonrelativistic open string excitations with winding number and demonstrate that their dynamics can be encoded into a local gauge theory in one higher dimension. By demanding conformal invariance of the boundary couplings, the nonlinear equations of motion that govern the consistent open string backgrounds coupled to an arbitrary closed background (described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field) are derived and shown to emerge from a Galilean invariant Dirac-Born-Infeld type action.
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References
D.H. Friedan, Nonlinear models in 2 + ϵ dimensions, Annals Phys. 163 (1985) 318 [INSPIRE].
R.G. Leigh, Dirac-Born-Infeld Action from Dirichlet Sigma Model, Mod. Phys. Lett. A 4 (1989) 2767 [INSPIRE].
C.G. Callan Jr., C. Lovelace, C.R. Nappi and S.A. Yost, String Loop Corrections to β-functions, Nucl. Phys. B 288 (1987) 525 [INSPIRE].
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 [Adv. Theor. Math. Phys. 4 (2000) 283] [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].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-duality, JHEP 11 (2018) 133 [arXiv:1806.06071] [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].
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].
R. Andringa, E. Bergshoeff, J. Gomis and M. de Roo, ‘Stringy’ Newton-Cartan Gravity, Class. Quant. Grav. 29 (2012) 235020 [arXiv:1206.5176] [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].
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].
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].
J. Gomis, J. Oh and Z. Yan, Nonrelativistic String Theory in Background Fields, JHEP 10 (2019) 101 [arXiv:1905.07315] [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].
N. Seiberg, L. Susskind and N. Toumbas, Strings in background electric field, space/time noncommutativity and a new noncritical string theory, JHEP 06 (2000) 021 [hep-th/0005040] [INSPIRE].
R. Gopakumar, J.M. Maldacena, S. Minwalla and A. Strominger, S duality and noncommutative gauge theory, JHEP 06 (2000) 036 [hep-th/0005048] [INSPIRE].
E.S. Santos, M. de Montigny, F.C. Khanna and A.E. Santana, Galilean covariant Lagrangian models, J. Phys. A 37 (2004) 9771 [INSPIRE].
E. Bergshoeff, J. Rosseel and T. Zojer, Non-relativistic fields from arbitrary contracting backgrounds, Class. Quant. Grav. 33 (2016) 175010 [arXiv:1512.06064] [INSPIRE].
G. Festuccia, D. Hansen, J. Hartong and N.A. Obers, Symmetries and Couplings of Non-Relativistic Electrodynamics, JHEP 11 (2016) 037 [arXiv:1607.01753] [INSPIRE].
C. Batlle, J. Gomis and D. Not, Extended Galilean symmetries of non-relativistic strings, JHEP 02 (2017) 049 [arXiv:1611.00026] [INSPIRE].
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007) [DOI] [INSPIRE].
A. Bagchi, R. Basu, A. Kakkar and A. Mehra, Galilean Yang-Mills Theory, JHEP 04 (2016) 051 [arXiv:1512.08375] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, T-duality in Nonrelativistic Open String Theory, JHEP 02 (2021) 087 [arXiv:2008.05493] [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].
Z. Yan and M. Yu, Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory, JHEP 03 (2020) 181 [arXiv:1912.03181] [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].
W. Kummer and D.V. Vassilevich, Renormalizability of the open string sigma model and emergence of D-branes, JHEP 07 (2000) 012 [hep-th/0006108] [INSPIRE].
A. Abouelsaood, C.G. Callan Jr., C.R. Nappi and S.A. Yost, Open Strings in Background Gauge Fields, Nucl. Phys. B 280 (1987) 599 [INSPIRE].
D. Roychowdhury, Probing tachyon kinks in Newton-Cartan background, Phys. Lett. B 795 (2019) 225 [arXiv:1903.05890] [INSPIRE].
D. Pereñiguez, p-brane Newton-Cartan geometry, J. Math. Phys. 60 (2019) 112501 [arXiv:1908.04801] [INSPIRE].
J. Klusoň, Non-Relativistic D-brane from T-duality Along Null Direction, JHEP 10 (2019) 153 [arXiv:1907.05662] [INSPIRE].
J. Klusoň, Unstable D-brane in Torsional Newton-Cartan Background, JHEP 09 (2020) 191 [arXiv:2001.11543] [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].
K. Banerjee, R. Basu and A. Mohan, Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure, JHEP 11 (2019) 041 [arXiv:1909.11993] [INSPIRE].
S. Chapman, L. Di, K.T. Grosvenor and Z. Yan, Renormalization of Galilean Electrodynamics, JHEP 10 (2020) 195 [arXiv:2007.03033] [INSPIRE].
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Gomis, J., Yan, Z. & Yu, M. Nonrelativistic open string and Yang-Mills theory. J. High Energ. Phys. 2021, 269 (2021). https://doi.org/10.1007/JHEP03(2021)269
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DOI: https://doi.org/10.1007/JHEP03(2021)269