Skip to main content
SpringerLink
Log in

Tree-level S-matrix elements from S-duality

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

Abstract

It has been speculated that the S-matrix elements of type IIB superstring theory satisfy the Ward identity associated with the S-duality. This indicates that a group of S-matrix elements at each loop level are invariant under the linear SL(2, R) transformations. If one evaluates one component of such S-dual multiplet, then all other components can be found by the simple use of the linear SL(2, R) transformations.

In this paper, we calculate the disk-level S-matrix element of one graviton(dilaton), one B-field and one gauge boson on the word volume of D3-brane. The S-dual multiplet corresponding to the graviton(dilaton) amplitude has three(six) components. In particular, the graviton multiplet has the S-matrix element of one graviton, one R-R two-form and one gauge boson, and the dilaton multiplet has the S-matrix element of one R-R scalar, one B-field and one gauge boson vertex operators. We calculate explicitly these particular components and show that they are precisely the ones predicted by the S-duality. We have also found the low energy contact terms of the dilaton multiplet at order α′2.

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. A. Font, L.E. Ibáñez, D. Lüst and F. Quevedo, Strong-weak coupling duality and nonperturbative effects in string theory, Phys. Lett. B 249 (1990) 35 [INSPIRE].

    ADS  Google Scholar 

  2. S.-J. Rey, The confining phase of superstrings and axionic strings, Phys. Rev. D 43 (1991) 526 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. A. Sen, Strong-weak coupling duality in four-dimensional string theory, Int. J. Mod. Phys. A 9 (1994) 3707 [hep-th/9402002] [INSPIRE].

    ADS  Google Scholar 

  4. A. Sen, Dyon-monopole bound states, selfdual harmonic forms on the multi - monopole moduli space and SL(2, \( \mathbb{Z} \)) invariance in string theory, Phys. Lett. B 329 (1994) 217 [hep-th/9402032] [INSPIRE].

    ADS  Google Scholar 

  5. J.H. Schwarz, Does string theory have a duality symmetry relating weak and strong coupling?, hep-th/9307121 [INSPIRE].

  6. C. Hull and P. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, Cambridge U.K. (2007), pg. 739.

    MATH  Google Scholar 

  8. M.R. Garousi, S-duality of S-matrix, JHEP 11 (2011) 016 [arXiv:1106.1714] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. M.B. Green and P. Vanhove, D instantons, strings and M-theory, Phys. Lett. B 408 (1997) 122 [hep-th/9704145] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. E. Kiritsis and B. Pioline, On R 4 threshold corrections in IIB string theory and (p, q) string instantons, Nucl. Phys. B 508 (1997) 509 [hep-th/9707018] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. M.B. Green, M. Gutperle and H.-h. Kwon, Sixteen fermion and related terms in M-theory on T 2, Phys. Lett. B 421 (1998) 149 [hep-th/9710151] [INSPIRE].

    ADS  Google Scholar 

  14. B. Pioline, A note on nonperturbative R 4 couplings, Phys. Lett. B 431 (1998) 73 [hep-th/9804023] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. M.B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  16. M.B. Green, H.-h. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].

    ADS  Google Scholar 

  17. N.A. Obers and B. Pioline, Eisenstein series in string theory, Class. Quant. Grav. 17 (2000) 1215 [hep-th/9910115] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. A. Sinha, The \( {\widehat{G}^4}{\lambda^{{16}}} \) term in IIB supergravity, JHEP 08 (2002) 017 [hep-th/0207070] [INSPIRE].

    Article  ADS  Google Scholar 

  19. N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 09 (2004) 047 [hep-th/0406055] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. E. D’Hoker and D. Phong, Two-loop superstrings VI: Non-renormalization theorems and the 4-point function, Nucl. Phys. B 715 (2005) 3 [hep-th/0501197] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. E. D’Hoker, M. Gutperle and D. Phong, Two-loop superstrings and S-duality, Nucl. Phys. B 722 (2005) 81 [hep-th/0503180] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. M.B. Green, J.G. Russo and P. Vanhove, Non-renormalisation conditions in type-II string theory and maximal supergravity, JHEP 02 (2007) 099 [hep-th/0610299] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. A. Basu, The D 4 R 4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106003 [arXiv:0708.2950] [INSPIRE].

    ADS  Google Scholar 

  25. A. Basu, The D 6 R 4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106004 [arXiv:0712.1252] [INSPIRE].

    ADS  Google Scholar 

  26. 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 

  27. A. Basu, Constraining the D3-brane effective action, JHEP 09 (2008) 124 [arXiv:0808.2060] [INSPIRE].

    Article  ADS  Google Scholar 

  28. M.R. Garousi, S-duality of D-brane action at order O(α′2), Phys. Lett. B 701 (2011) 465 [arXiv:1103.3121] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. M.R. Garousi, On S-duality of D 3 -brane S-matrix, Phys. Rev. D 84 (2011) 126019 [arXiv:1108.4782] [INSPIRE].

    ADS  Google Scholar 

  30. M.R. Garousi, S-duality of non-abelian S-matrix, arXiv:1109.5555 [INSPIRE].

  31. J. Cohn, D. Friedan, Z.-a. Qiu and S.H. Shenker, Covariant quantization of supersymmetric string theories: the spinor field of the Ramond-Neveu-Schwarz model, Nucl. Phys. B 278 (1986) 577 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. 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 

  33. M.R. Garousi and R.C. Myers, Superstring scattering from D-branes, Nucl. Phys. B 475 (1996) 193 [hep-th/9603194] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. A. Hashimoto and I.R. Klebanov, Scattering of strings from D-branes, Nucl. Phys. Proc. Suppl. 55B (1997) 118 [hep-th/9611214] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. S. Stieberger, Open & closed vs. pure open string disk amplitudes, arXiv:0907.2211 [INSPIRE].

  36. Y. Kitazawa, Effective Lagrangian for open superstring from five point function, Nucl. Phys. B 289 (1987) 599 [INSPIRE].

    Article  ADS  Google Scholar 

  37. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York U.S.A. (1994).

    MATH  Google Scholar 

  38. T. Huber and D. Maˆıtre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters, Comput. Phys. Commun. 175 (2006) 122 [hep-ph/0507094] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  39. M. Billó et al., Microscopic string analysis of the D0-D8-brane system and dual R-R states, Nucl. Phys. B 526 (1998) 199 [hep-th/9802088] [INSPIRE].

    Article  ADS  Google Scholar 

  40. H. Liu and J. Michelson, *-trek 3: the search for Ramond-Ramond couplings, Nucl. Phys. B 614 (2001) 330 [hep-th/0107172] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. M.R. Garousi and E. Hatefi, More on WZ action of non-BPS branes, JHEP 03 (2009) 008 [arXiv:0812.4216] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. M.R. Garousi and M. Mir, On RR couplings on D-branes at order O(α′2), JHEP 02 (2011) 008 [arXiv:1012.2747] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. G.W. Gibbons and D.A. Rasheed, SL(2, R) invariance of nonlinear electrodynamics coupled to an axion and a dilaton, Phys. Lett. B 365 (1996) 46 [hep-th/9509141] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  44. A.A. Tseytlin, Selfduality of Born-Infeld action and Dirichlet three-brane of type IIB superstring theory, Nucl. Phys. B 469 (1996) 51 [hep-th/9602064] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. M.B. Green and M. Gutperle, Comments on three-branes, Phys. Lett. B 377 (1996) 28 [hep-th/9602077] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  46. D. Haertl, O. Schlotterer and S. Stieberger, Higher point spin field correlators in D = 4 superstring theory, Nucl. Phys. B 834 (2010) 163 [arXiv:0911.5168] [INSPIRE].

    Article  ADS  Google Scholar 

  47. D. Haertl and O. Schlotterer, Higher loop spin field correlators in various dimensions, Nucl. Phys. B 849 (2011) 364 [arXiv:1011.1249] [INSPIRE].

    Article  ADS  Google Scholar 

  48. K. Becker, G. Guo and D. Robbins, Four-derivative brane couplings from string amplitudes, JHEP 12 (2011) 050 [arXiv:1110.3831] [INSPIRE].

    Article  ADS  Google Scholar 

  49. A. Hashimoto and I.R. Klebanov, Decay of excited D-branes, Phys. Lett. B 381 (1996) 437 [hep-th/9604065] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  50. M.R. Garousi and R.C. Myers, World volume interactions on D-branes, Nucl. Phys. B 542 (1999) 73 [hep-th/9809100] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. M.R. Garousi and M. Mir, Towards extending the Chern-Simons couplings at order O(α′2), JHEP 05 (2011) 066 [arXiv:1102.5510] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad, Iran

    Mohammad R. Garousi

Authors
  1. Mohammad R. Garousi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad R. Garousi.

Additional information

ArXiv ePrint: 1201.2556

Rights and permissions

Reprints and permissions

About this article

Cite this article

Garousi, M.R. Tree-level S-matrix elements from S-duality. J. High Energ. Phys. 2012, 140 (2012). https://doi.org/10.1007/JHEP04(2012)140

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2012)140

Keywords

Search

Navigation