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Large gauge transformations in double field theory

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Abstract

Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as ‘generalized coordinate transformations’ in the doubled space by proposing and testing a formula that writes large transformations in terms of derivatives of the coordinate maps. Successive generalized coordinate transformations give a generalized coordinate transformation that differs from the direct composition of the original two. Instead, it is constructed using the Courant bracket. These transformations form a group when acting on fields but, intriguingly, do not associate when acting on coordinates.

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References

  1. C. Hull and B. Zwiebach, Double field theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].

    ADS  Google Scholar 

  6. W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].

    ADS  Google Scholar 

  7. A.A. Tseytlin, Duality symmetric formulation of string world sheet dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. M.J. Duff, Duality rotations in string theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. M.J. Duff and J.X. Lu, Duality rotations in membrane theory, Nucl. Phys. B 347 (1990) 394 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. O. Hohm and S.K. Kwak, Frame-like geometry of double field theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. S.K. Kwak, Invariances and equations of motion in double field theory, JHEP 10 (2010) 047 [arXiv:1008.2746] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. O. Hohm, T-duality versus gauge symmetry, Prog. Theor. Phys. Suppl. 188 (2011) 116 [arXiv:1101.3484] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  14. B. Zwiebach, Double field theory, T-duality and courant brackets, Lect. Notes Phys. 851 (2012) 265 [arXiv:1109.1782] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. O. Hohm, On factorizations in perturbative quantum gravity, JHEP 04 (2011) 103 [arXiv:1103.0032] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. O. Hohm and S.K. Kwak, Double field theory formulation of heterotic strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. O. Hohm, S.K. Kwak and B. Zwiebach, Unification of type II strings and T-duality, Phys. Rev. Lett. 107 (2011) 171603 [arXiv:1106.5452] [INSPIRE].

    Article  ADS  Google Scholar 

  18. O. Hohm, S.K. Kwak and B. Zwiebach, Double field theory of Type II strings, JHEP 09 (2011) 013 [arXiv:1107.0008] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. O. Hohm and S.K. Kwak, Massive type II in double field theory, JHEP 11 (2011) 086 [arXiv:1108.4937] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. O. Hohm and S.K. Kwak, N = 1 supersymmetric double field theory, JHEP 03 (2012) 080 [arXiv:1111.7293] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. O. Hohm and B. Zwiebach, On the Riemann tensor in double field theory, JHEP 05 (2012) 126 [arXiv:1112.5296] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. C. Hillmann, Generalized E 7(7) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [arXiv:0901.1581] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. D.S. Berman, H. Godazgar and M.J. Perry, SO(5, 5) duality in M-theory and generalized geometry, Phys. Lett. B 700 (2011) 65 [arXiv:1103.5733] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. D.S. Berman, E.T. Musaev and M.J. Perry, Boundary terms in generalized geometry and doubled field theory, Phys. Lett. B 706 (2011) 228 [arXiv:1110.3097] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality invariant actions and generalised geometry, JHEP 02 (2012) 108 [arXiv:1111.0459] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. P. West, E 11 , generalised space-time and IIA string theory, Phys. Lett. B 696 (2011) 403 [arXiv:1009.2624] [INSPIRE].

    Article  ADS  Google Scholar 

  29. A. Rocen and P. West, E 11 , generalised space-time and IIA string theory: the RR sector, arXiv:1012.2744 [INSPIRE].

  30. I. Jeon, K. Lee and J.-H. Park, Differential geometry with a projection: Application to double field theory, JHEP 04 (2011) 014 [arXiv:1011.1324] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].

    ADS  Google Scholar 

  32. I. Jeon, K. Lee and J.-H. Park, Incorporation of fermions into double field theory, JHEP 11 (2011) 025 [arXiv:1109.2035] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. I. Jeon, K. Lee and J.-H. Park, Supersymmetric double field theory: stringy reformulation of supergravity, Phys. Rev. D 85 (2012) 081501 [Erratum ibid. D 86 (2012) 089903] [arXiv:1112.0069] [INSPIRE].

    ADS  Google Scholar 

  34. I. Jeon, K. Lee and J.-H. Park, Ramond-Ramond cohomology and O(D, D) T-duality, JHEP 09 (2012) 079 [arXiv:1206.3478] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. M.B. Schulz, T-folds, doubled geometry and the SU(2) WZW model, JHEP 06 (2012) 158 [arXiv:1106.6291] [INSPIRE].

    Article  ADS  Google Scholar 

  36. N.B. Copland, Connecting T-duality invariant theories, Nucl. Phys. B 854 (2012) 575 [arXiv:1106.1888] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. N.B. Copland, A double σ-model for double field theory, JHEP 04 (2012) 044 [arXiv:1111.1828] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. D.C. Thompson, Duality invariance: from M-theory to double field theory, JHEP 08 (2011) 125 [arXiv:1106.4036] [INSPIRE].

    Article  ADS  Google Scholar 

  39. C. Albertsson, S.-H. Dai, P.-W. Kao and F.-L. Lin, Double field theory for double D-branes, JHEP 09 (2011) 025 [arXiv:1107.0876] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].

    Article  ADS  Google Scholar 

  41. G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of double field theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].

    Article  ADS  Google Scholar 

  42. D. Geissbuhler, Double field theory and N = 4 gauged supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. M. Graña and D. Marques, Gauged double field theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].

    Article  ADS  Google Scholar 

  44. A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as generalised geometry I: type II theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. A. Coimbra, C. Strickland-Constable and D. Waldram, E d(d) × R + generalised geometry, connections and M-theory, arXiv:1112.3989 [INSPIRE].

  46. I. Vaisman, On the geometry of double field theory, J. Math. Phys. 53 (2012) 033509 [arXiv:1203.0836] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].

    Article  ADS  Google Scholar 

  48. D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-geometric fluxes in supergravity and double field theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  49. G. Dibitetto, J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. T. Kikuchi, T. Okada and Y. Sakatani, Rotating string in doubled geometry with generalized isometries, Phys. Rev. D 86 (2012) 046001 [arXiv:1205.5549] [INSPIRE].

    ADS  Google Scholar 

  51. E. Malek, U-duality in three and four dimensions, arXiv:1205.6403 [INSPIRE].

  52. M. Bruni, S. Matarrese, S. Mollerach and S. Sonego, Perturbations of space-time: gauge transformations and gauge invariance at second order and beyond, Class. Quant. Grav. 14 (1997) 2585 [gr-qc/9609040] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. L.R.W. Abramo, R.H. Brandenberger and V.F. Mukhanov, The energy-momentum tensor for cosmological perturbations, Phys. Rev. D 56 (1997) 3248 [gr-qc/9704037] [INSPIRE].

    ADS  Google Scholar 

  54. R. Blumenhagen and E. Plauschinn, Nonassociative gravity in string theory?, J. Phys. A 44 (2011) 015401 [arXiv:1010.1263] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  55. D. Lüst, T-duality and closed string non-commutative (doubled) geometry, JHEP 12 (2010) 084 [arXiv:1010.1361] [INSPIRE].

    Article  Google Scholar 

  56. R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric fluxes, asymmetric strings and nonassociative geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].

    ADS  Google Scholar 

  57. D. Mylonas, P. Schupp and R.J. Szabo, Membrane σ-models and quantization of non-geometric flux backgrounds, JHEP 09 (2012) 012 [arXiv:1207.0926] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. C. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Arnold Sommerfeld Center for Theoretical Physics, Theresienstrasse 37, D-80333, Munich, Germany

    Olaf Hohm

  2. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A

    Barton Zwiebach

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  1. Olaf Hohm
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  2. Barton Zwiebach
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Correspondence to Olaf Hohm.

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ArXiv ePrint: 1207.4198

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Hohm, O., Zwiebach, B. Large gauge transformations in double field theory. J. High Energ. Phys. 2013, 75 (2013). https://doi.org/10.1007/JHEP02(2013)075

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