Skip to main content
SpringerLink
Log in

The worldvolume action of kink solitons in AdS spacetime

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit “kink” solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters-associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic scalar curvature. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk spacetime.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Rajaraman, Solitons and instantons. An introduction to solitons and instantons in quantum field theory, North-holland, The Netherlands (1982).

  2. N.S. Manton and P. Sutcliffe, Topological solitons, Cambridge University Press, Cambridge U.K. (2004).

    Book  MATH  Google Scholar 

  3. E. Witten and D.I. Olive, Supersymmetry algebras that include topological charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].

    Article  ADS  Google Scholar 

  4. M. Duff, R.R. Khuri and J. Lu, String solitons, Phys. Rept. 259 (1995) 213 [hep-th/9412184] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. K. Stelle, Lectures on supergravity p-branes, hep-th/9701088 [INSPIRE].

  6. N.D. Antunes, E.J. Copeland, M. Hindmarsh and A. Lukas, Kinky brane worlds, Phys. Rev. D 68 (2003) 066005 [hep-th/0208219] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. M. Aganagic, C. Popescu and J.H. Schwarz, Gauge invariant and gauge fixed D-brane actions, Nucl. Phys. B 495 (1997) 99 [hep-th/9612080] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. T. Adawi, M. Cederwall, U. Gran, M. Holm and B.E. Nilsson, Superembeddings, nonlinear supersymmetry and five-branes, Int. J. Mod. Phys. A 13 (1998) 4691 [hep-th/9711203] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. D.P. Sorokin, Superbranes and superembeddings, Phys. Rept. 329 (2000) 1 [hep-th/9906142][INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. P.S. Howe, A. Kaya, E. Sezgin and P. Sundell, Codimension one-branes, Nucl. Phys. B 587 (2000) 481 [hep-th/0001169] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. J.-P. Derendinger and R. Sauser, A five-brane modulus in the effective N = 1 supergravity of M-theory, Nucl. Phys. B 598 (2001) 87 [hep-th/0009054] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. D.P. George and R.R. Volkas, Dynamics of the infinitely-thin kink, Phys. Lett. B 704 (2011) 646 [arXiv:0911.0538] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. R. Gregory, Effective actions for bosonic topological defects, Phys. Rev. D 43 (1991) 520 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. A. Larsen, Comment on thickness corrections to Nambu wall, Phys. Lett. A 181 (1993) 369 [hep-th/9306046] [INSPIRE].

    Article  ADS  Google Scholar 

  15. C. Barrabes, B. Boisseau and M. Sakellariadou, Gravitational effects on domain walls with curvature corrections, Phys. Rev. D 49 (1994) 2734 [gr-qc/9307008] [INSPIRE].

    ADS  Google Scholar 

  16. B. Carter and R. Gregory, Curvature corrections to dynamics of domain walls, Phys. Rev. D 51 (1995) 5839 [hep-th/9410095] [INSPIRE].

    ADS  Google Scholar 

  17. H. Arodz, Collective dynamics of a domain wall: an outline, hep-ph/9709241 [INSPIRE].

  18. F. Bonjour, C. Charmousis and R. Gregory, The dynamics of curved gravitating walls, Phys. Rev. D 62 (2000) 083504 [gr-qc/0002063] [INSPIRE].

    ADS  Google Scholar 

  19. Y. Burnier and K. Zuleta, Effective action of a five-dimensional domain wall, JHEP 05 (2009) 065 [arXiv:0812.2227] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. C.P. Bachas, P. Bain and M.B. Green, Curvature terms in D-brane actions and their M-theory origin, JHEP 05 (1999) 011 [hep-th/9903210] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. A. Fotopoulos, On (α′)2 corrections to the D-brane action for nongeodesic world volume embeddings, JHEP 09 (2001) 005 [hep-th/0104146] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. N. Wyllard, Derivative corrections to the D-brane Born-Infeld action: Nongeodesic embeddings and the Seiberg-Witten map, JHEP 08 (2001) 027 [hep-th/0107185] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. N. Wyllard, Derivative corrections to D-brane actions with constant background fields, Nucl. Phys. B 598 (2001) 247 [hep-th/0008125] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. O. Andreev and A.A. Tseytlin, Partition function representation for the open superstring effective action: cancellation of Mobius infinities and derivative corrections to Born-Infeld lagrangian, Nucl. Phys. B 311 (1988) 205 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Bilal, Higher derivative corrections to the non-abelian Born-Infeld action, Nucl. Phys. B 618 (2001) 21 [hep-th/0106062] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. P.S. Howe and U. Lindström, Kappa symmetric higher derivative terms in brane actions, Class. Quant. Grav. 19 (2002) 2813 [hep-th/0111036] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  27. Y.-K.E. Cheung, M. Laidlaw and K. Savvidy, Open string gravity?, JHEP 12 (2004) 028 [hep-th/0406245] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. D.V. Belyaev and T.G. Pugh, The supermultiplet of boundary conditions in supergravity, JHEP 10 (2010) 031 [arXiv:1008.1574] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. G. Dvali, G. Gabadadze and M. Porrati, 4D gravity on a brane in 5D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. G.W. Horndeski, The most general scalar tensor theory with second order field equations, Int. J. Theor. Phys. 10 (1974) 363.

    Article  MathSciNet  Google Scholar 

  31. C. Charmousis, E.J. Copeland, A. Padilla and P.M. Saffin, General second order scalar-tensor theory, self tuning and the Fab Four, Phys. Rev. Lett. 108 (2012) 051101 [arXiv:1106.2000] [INSPIRE].

    Article  ADS  Google Scholar 

  32. F. Mueller-Hoissen, Gravity actions, boundary terms and second order field equations, Nucl. Phys. B 337 (1990) 709 [INSPIRE].

    Article  ADS  Google Scholar 

  33. C. Cartier, J.-c. Hwang and E.J. Copeland, Evolution of cosmological perturbations in nonsingular string cosmologies, Phys. Rev. D 64 (2001) 103504 [astro-ph/0106197] [INSPIRE].

    ADS  Google Scholar 

  34. C. Charmousis, S.C. Davis and J.-F. Dufaux, Scalar brane backgrounds in higher order curvature gravity, JHEP 12 (2003) 029 [hep-th/0309083] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. L. Amendola, C. Charmousis and S.C. Davis, Constraints on Gauss-Bonnet gravity in dark energy cosmologies, JCAP 12 (2006) 020 [hep-th/0506137] [INSPIRE].

    Article  ADS  Google Scholar 

  36. A. Nicolis, R. Rattazzi and E. Trincherini, The galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  37. A. Nicolis and R. Rattazzi, Classical and quantum consistency of the DGP model, JHEP 06 (2004) 059 [hep-th/0404159] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. S. Endlich, K. Hinterbichler, L. Hui, A. Nicolis and J. Wang, Derrick’s theorem beyond a potential, JHEP 05 (2011) 073 [arXiv:1002.4873] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. P. Creminelli, M.A. Luty, A. Nicolis and L. Senatore, Starting the universe: stable violation of the null energy condition and non-standard cosmologies, JHEP 12 (2006) 080 [hep-th/0606090] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP 05 (2010) 095 [Erratum ibid. 1111 (2011) 128] [arXiv:0912.4258] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. N. Arkani-Hamed, H.-C. Cheng, M.A. Luty and S. Mukohyama, Ghost condensation and a consistent infrared modification of gravity, JHEP 05 (2004) 074 [hep-th/0312099] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  42. J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P(X,Ф) and the ghost condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].

    ADS  Google Scholar 

  43. J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric galileons, Phys. Rev. D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].

    ADS  Google Scholar 

  44. E.I. Buchbinder, J. Khoury and B.A. Ovrut, New ekpyrotic cosmology, Phys. Rev. D 76 (2007) 123503 [hep-th/0702154] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  45. P. Creminelli and L. Senatore, A smooth bouncing cosmology with scale invariant spectrum, JCAP 11 (2007) 010 [hep-th/0702165] [INSPIRE].

    Article  ADS  Google Scholar 

  46. E.I. Buchbinder, J. Khoury and B.A. Ovrut, On the initial conditions in new ekpyrotic cosmology, JHEP 11 (2007) 076 [arXiv:0706.3903] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. E.I. Buchbinder, J. Khoury and B.A. Ovrut, Non-gaussianities in new ekpyrotic cosmology, Phys. Rev. Lett. 100 (2008) 171302 [arXiv:0710.5172] [INSPIRE].

    Article  ADS  Google Scholar 

  48. C. Lin, R.H. Brandenberger and L. Levasseur Perreault, A matter bounce by means of ghost condensation, JCAP 04 (2011) 019 [arXiv:1007.2654] [INSPIRE].

    Article  ADS  Google Scholar 

  49. L. Levasseur Perreault, R. Brandenberger and A.-C. Davis, Defrosting in an emergent galileon cosmology, Phys. Rev. D 84 (2011) 103512 [arXiv:1105.5649] [INSPIRE].

    ADS  Google Scholar 

  50. P. Creminelli, A. Nicolis and E. Trincherini, Galilean genesis: an alternative to inflation, JCAP 11 (2010) 021 [arXiv:1007.0027] [INSPIRE].

    Article  ADS  Google Scholar 

  51. C. de Rham and A.J. Tolley, DBI and the galileon reunited, JCAP 05 (2010) 015 [arXiv:1003.5917] [INSPIRE].

    Article  Google Scholar 

  52. M. Trodden and K. Hinterbichler, Generalizing galileons, Class. Quant. Grav. 28 (2011) 204003 [arXiv:1104.2088] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. K. Hinterbichler, M. Trodden and D. Wesley, Multi-field galileons and higher co-dimension branes, Phys. Rev. D 82 (2010) 124018 [arXiv:1008.1305] [INSPIRE].

    ADS  Google Scholar 

  54. G.L. Goon, K. Hinterbichler and M. Trodden, Stability and superluminality of spherical DBI galileon solutions, Phys. Rev. D 83 (2011) 085015 [arXiv:1008.4580] [INSPIRE].

    ADS  Google Scholar 

  55. A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  57. L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  58. O. DeWolfe, D. Freedman, S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  59. M. Gremm, Four-dimensional gravity on a thick domain wall, Phys. Lett. B 478 (2000) 434 [hep-th/9912060] [INSPIRE].

    Article  ADS  Google Scholar 

  60. M. Gremm, Thick domain walls and singular spaces, Phys. Rev. D 62 (2000) 044017 [hep-th/0002040] [INSPIRE].

    ADS  Google Scholar 

  61. A. Lukas, B.A. Ovrut, K. Stelle and D. Waldram, The universe as a domain wall, Phys. Rev. D 59 (1999) 086001 [hep-th/9803235] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  62. A. Lukas, B.A. Ovrut, K. Stelle and D. Waldram, Heterotic M-theory in five-dimensions, Nucl. Phys. B 552 (1999) 246 [hep-th/9806051] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. B.A. Ovrut, T. Pantev and J. Park, Small instanton transitions in heterotic M-theory, JHEP 05 (2000) 045 [hep-th/0001133] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok, The ekpyrotic universe: colliding branes and the origin of the hot Big Bang, Phys. Rev. D 64 (2001) 123522 [hep-th/0103239] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  65. R.Y. Donagi, J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok, Visible branes with negative tension in heterotic M-theory, JHEP 11 (2001) 041 [hep-th/0105199] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. J. Khoury, B.A. Ovrut, N. Seiberg, P.J. Steinhardt and N. Turok, From Big Crunch to Big Bang, Phys. Rev. D 65 (2002) 086007 [hep-th/0108187] [INSPIRE].

    ADS  Google Scholar 

  67. A. Kehagias and K. Tamvakis, Localized gravitons, gauge bosons and chiral fermions in smooth spaces generated by a bounce, Phys. Lett. B 504 (2001) 38 [hep-th/0010112] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. M. Shaposhnikov, P. Tinyakov and K. Zuleta, The fate of the zero mode of the five-dimensional kink in the presence of gravity, JHEP 09 (2005) 062 [hep-th/0508102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  69. C. Charmousis and R. Zegers, Matching conditions for a brane of arbitrary codimension, JHEP 08 (2005) 075 [hep-th/0502170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  70. B.A. Ovrut and J. Stokes, Heterotic kink solitons and their worldvolume action, arXiv:1205.4236 [INSPIRE].

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104-6396, U.S.A.

    Justin Khoury, Burt A. Ovrut & James Stokes

Authors
  1. Justin Khoury
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Burt A. Ovrut
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James Stokes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Justin Khoury.

Additional information

ArXiv ePrint: 1203.4562

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khoury, J., Ovrut, B.A. & Stokes, J. The worldvolume action of kink solitons in AdS spacetime. J. High Energ. Phys. 2012, 15 (2012). https://doi.org/10.1007/JHEP08(2012)015

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP08(2012)015

Keywords

Search

Navigation