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Journal of High Energy Physics

, 2019:71 | Cite as

Relating non-relativistic string theories

  • Troels Harmark
  • Jelle Hartong
  • Lorenzo Menculini
  • Niels A. Obers
  • Gerben OlingEmail author
Open Access
Regular Article - Theoretical Physics
  • 21 Downloads

Abstract

Non-relativistic string theories promise to provide simpler theories of quantum gravity as well as tractable limits of the AdS/CFT correspondence. However, several apparently distinct non-relativistic string theories have been constructed. In particular, one approach is to reduce a relativistic string along a null isometry in target space. Another method is to perform an appropriate large speed of light expansion of a relativistic string. Both of the resulting non-relativistic string theories only have a well-defined spectrum if they have nonzero winding along a longitudinal spatial direction. In the presence of a Kalb-Ramond field, we show that these theories are equivalent provided the latter direction is an isometry. Finally, we consider a further limit of non-relativistic string theory that has proven useful in the context of AdS/CFT (related to Spin Matrix Theory). In that case, the worldsheet theory itself becomes non-relativistic and the dilaton coupling vanishes.

Keywords

AdS-CFT Correspondence Conformal Field Models in String Theory Gauge-gravity correspondence String Duality 

Notes

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

References

  1. [1]
    R. Andringa, E. Bergshoeff, S. Panda and M. de Roo, Newtonian Gravity and the Bargmann Algebra, Class. Quant. Grav.28 (2011) 105011 [arXiv:1011.1145] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    M.H. Christensen, J. Hartong, N.A. Obers and B. Rollier, Torsional Newton-Cartan Geometry and Lifshitz Holography, Phys. Rev.D 89 (2014) 061901 [arXiv:1311.4794] [INSPIRE].
  3. [3]
    M.H. Christensen, J. Hartong, N.A. Obers and B. Rollier, Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography, JHEP01 (2014) 057 [arXiv:1311.6471] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    J. Hartong, E. Kiritsis and N.A. Obers, Schrödinger Invariance from Lifshitz Isometries in Holography and Field Theory, Phys. Rev.D 92 (2015) 066003 [arXiv:1409.1522] [INSPIRE].
  5. [5]
    K. Jensen, On the coupling of Galilean-invariant field theories to curved spacetime, SciPost Phys.5 (2018) 011 [arXiv:1408.6855] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    J. Hartong, E. Kiritsis and N.A. Obers, Lifshitz space-times for Schrödinger holography, Phys. Lett.B 746 (2015) 318 [arXiv:1409.1519] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    D.T. Son, Newton-Cartan Geometry and the Quantum Hall Effect, arXiv:1306.0638 [INSPIRE].
  8. [8]
    M. Geracie, D.T. Son, C. Wu and S.-F. Wu, Spacetime Symmetries of the Quantum Hall Effect, Phys. Rev.D 91 (2015) 045030 [arXiv:1407.1252] [INSPIRE].
  9. [9]
    A. Gromov and A.G. Abanov, Thermal Hall Effect and Geometry with Torsion, Phys. Rev. Lett.114 (2015) 016802 [arXiv:1407.2908] [INSPIRE].
  10. [10]
    M. Geracie, K. Prabhu and M.M. Roberts, Curved non-relativistic spacetimes, Newtonian gravitation and massive matter, J. Math. Phys.56 (2015) 103505 [arXiv:1503.02682] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    R. Andringa, E. Bergshoeff, J. Gomis and M. de Roo, ‘Stringy’ Newton-Cartan Gravity, Class. Quant. Grav.29 (2012) 235020 [arXiv:1206.5176] [INSPIRE].
  12. [12]
    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].
  13. [13]
    J. Klusoň, Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction, JHEP05 (2018) 041 [arXiv:1803.07336] [INSPIRE].
  14. [14]
    E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-duality, JHEP11 (2018) 133 [arXiv:1806.06071] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    J. Klusoň, Nonrelativistic String Theory σ-model and Its Canonical Formulation, Eur. Phys. J.C 79 (2019) 108 [arXiv:1809.10411] [INSPIRE].
  16. [16]
    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, JHEP11 (2018) 190 [arXiv:1810.05560] [INSPIRE].
  17. [17]
    J. Klusoň, (m, n)-String and D1-Brane in Stringy Newton-Cartan Background, JHEP04 (2019) 163 [arXiv:1901.11292] [INSPIRE].
  18. [18]
    J. Gomis, J. Oh and Z. Yan, Nonrelativistic String Theory in Background Fields, JHEP10 (2019) 101 [arXiv:1905.07315] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A.D. Gallegos, U. Gürsoy and N. Zinnato, Torsional Newton Cartan gravity from non-relativistic strings, arXiv:1906.01607 [INSPIRE].
  20. [20]
    J. Hartong and N.A. Obers, Hǒrava-Lifshitz gravity from dynamical Newton-Cartan geometry, JHEP07 (2015) 155 [arXiv:1504.07461] [INSPIRE].
  21. [21]
    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].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    H.R. Afshar, E.A. Bergshoeff, A. Mehra, P. Parekh and B. Rollier, A Schrödinger approach to Newton-Cartan and Hǒrava-Lifshitz gravities, JHEP04 (2016) 145 [arXiv:1512.06277] [INSPIRE].ADSzbMATHGoogle Scholar
  23. [23]
    E.A. Bergshoeff and J. Rosseel, Three-Dimensional Extended Bargmann Supergravity, Phys. Rev. Lett.116 (2016) 251601 [arXiv:1604.08042] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J. Hartong, Y. Lei and N.A. Obers, Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity, Phys. Rev.D 94 (2016) 065027 [arXiv:1604.08054] [INSPIRE].
  25. [25]
    D. Van den Bleeken, Torsional Newton-Cartan gravity from the large c expansion of general relativity, Class. Quant. Grav.34 (2017) 185004 [arXiv:1703.03459] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    E. Bergshoeff, A. Chatzistavrakidis, L. Romano and J. Rosseel, Newton-Cartan Gravity and Torsion, JHEP10 (2017) 194 [arXiv:1708.05414] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    J. Hartong, Y. Lei, N.A. Obers and G. Oling, Zooming in on AdS 3/C F T 2near a BPS bound, JHEP05 (2018) 016 [arXiv:1712.05794] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    L. Avilés, E. Frodden, J. Gomis, D. Hidalgo and J. Zanelli, Non-Relativistic Maxwell Chern-Simons Gravity, JHEP05 (2018) 047 [arXiv:1802.08453] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    D. Hansen, J. Hartong and N.A. Obers, Action Principle for Newtonian Gravity, Phys. Rev. Lett.122 (2019) 061106 [arXiv:1807.04765] [INSPIRE].
  30. [30]
    E.A. Bergshoeff, K.T. Grosvenor, C. Simsek and Z. Yan, An Action for Extended String Newton-Cartan Gravity, JHEP01 (2019) 178 [arXiv:1810.09387] [INSPIRE].
  31. [31]
    M. Cariglia, General theory of Galilean gravity, Phys. Rev.D 98 (2018) 084057 [arXiv:1811.03446] [INSPIRE].
  32. [32]
    J. Matulich, S. Prohazka and J. Salzer, Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension, JHEP07 (2019) 118 [arXiv:1903.09165] [INSPIRE].
  33. [33]
    D. Van den Bleeken, Torsional Newton-Cartan gravity and strong gravitational fields, in 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (MG15), Rome, Italy, 1–7 July 2018 (2019) [arXiv:1903.10682] [INSPIRE].
  34. [34]
    D. Hansen, J. Hartong and N.A. Obers, Gravity between Newton and Einstein, arXiv:1904.05706 [INSPIRE].
  35. [35]
    E. Bergshoeff, J.M. Izquierdo, T. Ortín and L. Romano, Lie Algebra Expansions and Actions for Non-Relativistic Gravity, JHEP08 (2019) 048 [arXiv:1904.08304] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    J.A. de Azcárraga, D. Gútiez and J.M. Izquierdo, Extended D = 3 Bargmann supergravity from a Lie algebra expansion, arXiv:1904.12786 [INSPIRE].
  37. [37]
    D. Hansen, J. Hartong and N.A. Obers, Non-relativistic expansion of the Einstein-Hilbert Lagrangian, in 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (MG15), Rome, Italy, 1–7 July 2018 (2019) [arXiv:1905.13723] [INSPIRE].
  38. [38]
    P. Concha and E. Rodŕıguez, Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra, JHEP07 (2019) 085 [arXiv:1906.00086] [INSPIRE].
  39. [39]
    D.M. Peñafiel and P. Salgado-ReboLledó, Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra, arXiv:1906.02161 [INSPIRE].
  40. [40]
    D. Hansen, J. Hartong and N.A. Obers, Non-relativistic Gravity, to appear.Google Scholar
  41. [41]
    J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys.42 (2001) 3127 [hep-th/0009181] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    U.H. Danielsson, A. Guijosa and M. Kruczenski, IIA/B, wound and wrapped, JHEP10 (2000) 020 [hep-th/0009182] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    T. Harmark, K.R. Kristjansson and M. Orselli, Matching gauge theory and string theory in a decoupling limit of AdS/CFT, JHEP02 (2009) 027 [arXiv:0806.3370] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    T. Harmark and M. Orselli, Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence, JHEP11 (2014) 134 [arXiv:1409.4417] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    S.M. Ko, C. Melby-Thompson, R. Meyer and J.-H. Park, Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory, JHEP12 (2015) 144 [arXiv:1508.01121] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    K. Morand and J.-H. Park, Classification of non-Riemannian doubled-yet-gauged spacetime, Eur. Phys. J.C 77 (2017) 685 [Erratum ibid.C 78 (2018) 901] [arXiv:1707.03713] [INSPIRE].
  47. [47]
    D.S. Berman, C.D.A. Blair and R. Otsuki, Non-Riemannian geometry of M-theory, JHEP07 (2019) 175 [arXiv:1902.01867] [INSPIRE].
  48. [48]
    M. Kruczenski, Spin chains and string theory, Phys. Rev. Lett.93 (2004) 161602 [hep-th/0311203] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    J. Gomis, J. Gomis and K. Kamimura, Non-relativistic superstrings: A New soluble sector of AdS 5× S 5 , JHEP12 (2005) 024 [hep-th/0507036] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    A. Bagchi and R. Gopakumar, Galilean Conformal Algebras and AdS/CFT, JHEP07 (2009) 037 [arXiv:0902.1385] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  51. [51]
    G. Festuccia, D. Hansen, J. Hartong and N.A. Obers, Symmetries and Couplings of Non-Relativistic Electrodynamics, JHEP11 (2016) 037 [arXiv:1607.01753] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  52. [52]
    C. Duval, G. Burdet, H.P. Kunzle and M. Perrin, Bargmann Structures and Newton-cartan Theory, Phys. Rev.D 31 (1985) 1841 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    K. Jensen and A. Karch, Revisiting non-relativistic limits, JHEP04 (2015) 155 [arXiv:1412.2738] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    J. Klusoň, Note About Canonical Description of T-duality Along Light-Like Isometry, arXiv:1905.12910 [INSPIRE].
  55. [55]
    J. Isberg, U. Lindström, B. Sundborg and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys.B 411 (1994) 122 [hep-th/9307108] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    M. Rǒcek and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys.B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
  57. [57]
    J. Klusoň, Note About T-duality of Non-Relativistic String, JHEP08 (2019) 074 [arXiv:1811.12658] [INSPIRE].
  58. [58]
    C.D.A. Blair, A worldsheet supersymmetric Newton-Cartan string, arXiv:1908.00074 [INSPIRE].
  59. [59]
    J. Kluson, Hamiltonian Analysis of Non-Relativistic Non-BPS Dp-brane, JHEP07 (2017) 007 [arXiv:1704.08003] [INSPIRE].
  60. [60]
    J. Kluson, Remark About Non-Relativistic p-Brane, Eur. Phys. J.C 78 (2018) 27 [arXiv:1707.04034] [INSPIRE].
  61. [61]
    J. Kluson, Note about Hamiltonian formalism for Newton-Cartan string and p-brane, Eur. Phys. J.C 78 (2018) 511 [arXiv:1712.07430] [INSPIRE].
  62. [62]
    D. Roychowdhury, On integrability in nonrelativistic string theory, arXiv:1904.06485 [INSPIRE].
  63. [63]
    D. Roychowdhury, Nonrelativistic pulsating strings, JHEP09 (2019) 002 [arXiv:1907.00584] [INSPIRE].
  64. [64]
    T. Harmark, Interacting Giant Gravitons from Spin Matrix Theory, Phys. Rev.D 94 (2016) 066001 [arXiv:1606.06296] [INSPIRE].
  65. [65]
    J.A. de Azcarraga, J.M. Izquierdo, M. Picón and O. Varela, Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity, Nucl. Phys.B 662 (2003) 185 [hep-th/0212347] [INSPIRE].
  66. [66]
    F. Izaurieta, E. Rodriguez and P. Salgado, Expanding Lie (super)algebras through Abelian semigroups, J. Math. Phys.47 (2006) 123512 [hep-th/0606215] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    O. Khasanov and S. Kuperstein, (In)finite extensions of algebras from their Inonu-Wigner contractions, J. Phys.A 44 (2011) 475202 [arXiv:1103.3447] [INSPIRE].
  68. [68]
    J. Gomis, A. Kleinschmidt and J. Palmkvist, Galilean free Lie algebras, JHEP09 (2019) 109 [arXiv:1907.00410] [INSPIRE].
  69. [69]
    N. Ozdemir, M. Ozkan, O. Tunca and U. Zorba, Three-Dimensional Extended Newtonian (Super)Gravity, JHEP05 (2019) 130 [arXiv:1903.09377] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  70. [70]
    C. Hull and B. Zwiebach, Double Field Theory, JHEP09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  71. [71]
    O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP08 (2010) 008 [arXiv:1006.4823] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.The Niels Bohr InstituteUniversity of CopenhagenCopenhagen ØDenmark
  2. 2.School of Mathematics and Maxwell Institute for Mathematical SciencesUniversity of EdinburghEdinburghU.K.
  3. 3.Dipartimento di Fisica e GeologiaUniversità di Perugia, I.N.F.N. Sezione di PerugiaPerugiaItaly
  4. 4.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden

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