Abstract
The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic α ′N order terms, it is necessary to know the open string (tree level) (N + 2)-point amplitude of massless bosons, at least expanded at that order in α ′. In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring n-point amplitude is needed to find all the α ′N order terms. In this ‘revisited’ S-matrix approach we have checked that, at least up to α ′4 order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian. The sort of results that we obtain seem to agree completely with the ones achieved by the method of BPS configurations, proposed about ten years ago. By means of the KLT relations, our results can be mapped to the NS-NS sector of the low energy effective lagrangian of the type II string theories implying that there one can also find kinematical constraints in the N-point amplitudes and that important informations can be inferred, at least up to α ′4 order, by only using the (tree level) 4-point amplitude.
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References
J. Scherk and J.H. Schwarz, Dual models for nonhadrons, Nucl. Phys. B 81 (1974) 118 [INSPIRE].
C.G. Callan Jr., E. Martinec, M. Perry and D. Friedan, Strings in background fields, Nucl. Phys. B 262 (1985) 593 [INSPIRE].
A.A. Tseytlin, Vector field effective action in the open superstring theory, Nucl. Phys. B 276 (1986) 391 [Erratum ibid. B 291 (1987) 876] [INSPIRE].
D.J. Gross and E. Witten, Superstring modifications of Einstein’s equations, Nucl. Phys. B 277 (1986) 1 [INSPIRE].
E. Fradkin and A.A. Tseytlin, Nonlinear electrodynamics from quantized strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].
A. Abouelsaood, C.G. Callan Jr., C. Nappi and S. Yost, Open strings in background gauge fields, Nucl. Phys. B 280 (1987) 599 [INSPIRE].
E. Bergshoeff, E. Sezgin, C. Pope and P. Townsend, The Born-Infeld action from conformal invariance of the open superstring, Phys. Lett. B 188 (1987) 70 [INSPIRE].
R. Leigh, Dirac-Born-Infeld action from Dirichlet σ-model, Mod. Phys. Lett. A 4 (1989) 2767 [INSPIRE].
M. Cederwall and A. Karlsson, Pure spinor superfields and Born-Infeld theory, JHEP 11 (2011) 134 [arXiv:1109.0809] [INSPIRE].
A.A. Tseytlin, On nonabelian generalization of Born-Infeld action in string theory, Nucl. Phys. B 501 (1997) 41 [hep-th/9701125] [INSPIRE].
Y. Kitazawa, Effective Lagrangian for open superstring from five point function, Nucl. Phys. B 289 (1987) 599 [INSPIRE].
A. Bilal, Higher derivative corrections to the nonabelian Born-Infeld action, Nucl. Phys. B 618 (2001) 21 [hep-th/0106062] [INSPIRE].
A. Refolli, A. Santambrogio, N. Terzi and D. Zanon, F 5 contributions to the nonabelian Born-Infeld action from a supersymmetric Yang-Mills five point function, Nucl. Phys. B 613 (2001) 64 [Erratum ibid. B 648 (2003) 453-454] [hep-th/0105277] [INSPIRE].
P. Koerber and A. Sevrin, The nonabelian Born-Infeld action through order α ′3, JHEP 10 (2001) 003 [hep-th/0108169] [INSPIRE].
A. Collinucci, M. De Roo and M. Eenink, Supersymmetric Yang-Mills theory at order alpha ′3, JHEP 06 (2002) 024 [hep-th/0205150] [INSPIRE].
R. Medina, F.T. Brandt and F.R. Machado, The open superstring five point amplitude revisited, JHEP 07 (2002) 071 [hep-th/0208121] [INSPIRE].
E. Bergshoeff, A. Bilal, M. de Roo and A. Sevrin, Supersymmetric nonabelian Born-Infeld revisited, JHEP 07 (2001) 029 [hep-th/0105274] [INSPIRE].
O. Chandía and R. Medina, Four point effective actions in open and closed superstring theory, JHEP 11 (2003) 003 [hep-th/0310015] [INSPIRE].
L.A. Barreiro and R. Medina, 5-field terms in the open superstring effective action, JHEP 03 (2005) 055 [hep-th/0503182] [INSPIRE].
E. Hatefi, On effective actions of BPS branes and their higher derivative corrections, JHEP 05 (2010) 080 [arXiv:1003.0314] [INSPIRE].
J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].
N. Wyllard, Derivative corrections to D-brane actions with constant background fields, Nucl. Phys. B 598 (2001) 247 [hep-th/0008125] [INSPIRE].
O. Andreev, More about partition function of open bosonic string in background fields and string theory effective action, Phys. Lett. B 513 (2001) 207 [hep-th/0104061] [INSPIRE].
P. Koerber and A. Sevrin, The nonabelian D-brane effective action through order α ′4, JHEP 10 (2002) 046 [hep-th/0208044] [INSPIRE].
M. de Roo and M.G. Eenink, The effective action for the four point functions in abelian open superstring theory, JHEP 08 (2003) 036 [hep-th/0307211] [INSPIRE].
L. De Fosse, P. Koerber and A. Sevrin, The uniqueness of the abelian Born-Infeld action, Nucl. Phys. B 603 (2001) 413 [hep-th/0103015] [INSPIRE].
D.T. Grasso, Higher order contributions to the effective action of N = 4 super Yang-Mills, JHEP 11 (2002) 012 [hep-th/0210146] [INSPIRE].
M. Cederwall, B.E. Nilsson and D. Tsimpis, D = 10 super Yang-Mills at O(α ′2), JHEP 07 (2001) 042 [hep-th/0104236] [INSPIRE].
M. Cederwall, B.E. Nilsson and D. Tsimpis, The structure of maximally supersymmetric Yang-Mills theory: constraining higher order corrections, JHEP 06 (2001) 034 [hep-th/0102009] [INSPIRE].
J. Drummond, P. Heslop, P. Howe and S. Kerstan, Integral invariants in N = 4 SYM and the effective action for coincident D-branes, JHEP 08 (2003) 016 [hep-th/0305202] [INSPIRE].
D.T. Grasso, Higher order contributions to the effective action of N = 2 super Yang-Mills, JHEP 09 (2004) 054 [hep-th/0407264] [INSPIRE].
M. Movshev and A. Schwarz, Supersymmetric deformations of maximally supersymmetric gauge theories, JHEP 09 (2012) 136 [arXiv:0910.0620] [INSPIRE].
P. Howe, U. Lindström and L. Wulff, D = 10 supersymmetric Yang-Mills theory at α ′4, JHEP 07 (2010) 028 [arXiv:1004.3466] [INSPIRE].
P. Koerber and A. Sevrin, Testing the (α ′)3 term in the nonabelian open superstring effective action, JHEP 09 (2001) 009 [hep-th/0109030] [INSPIRE].
P. Koerber, Abelian and non-abelian D-brane effective actions, Fortsch. Phys. 52 (2004) 871 [hep-th/0405227] [INSPIRE].
E. Hatefi, On higher derivative corrections to Wess-Zumino and tachyonic actions in type-II super string theory, Phys. Rev. D 86 (2012) 046003 [arXiv:1203.1329] [INSPIRE].
M.R. Garousi and E. Hatefi, On Wess-Zumino terms of brane-antibrane systems, Nucl. Phys. B 800 (2008) 502 [arXiv:0710.5875] [INSPIRE].
M.R. Garousi and E. Hatefi, More on W Z action of non-BPS branes, JHEP 03 (2009) 008 [arXiv:0812.4216] [INSPIRE].
E. Hatefi and I. Park, More on closed string induced higher derivative interactions on D-branes, Phys. Rev. D 85 (2012) 125039 [arXiv:1203.5553] [INSPIRE].
E. Hatefi and I. Park, Universality in all-order α ′ corrections to BPS/non-BPS brane world volume theories, Nucl. Phys. B 864 (2012) 640 [arXiv:1205.5079] [INSPIRE].
A. Collinucci, M. de Roo and M.G. Eenink, Derivative corrections in ten-dimensional superMaxwell theory, JHEP 01 (2003) 039 [hep-th/0212012] [INSPIRE].
H. Kawai, D. Lewellen and S. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
J.H. Schwarz, Superstring theory, Phys. Rept. 89 (1982) 233.
M.B. Green, J.H. Schwarz, and E. Witten, Superstring theory vol. 1: introduction, Cambridge University Press, Cambridge U.K. (1987).
J. Polchinski, String theory, vol. 1: an introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998).
N. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal basis for gauge theory amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
S. Stieberger, Open & closed vs. Pure open string disk amplitudes, arXiv:0907.2211 [INSPIRE].
E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
J. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Complete n-point superstring disk amplitude II. Amplitude and hypergeometric function structure, arXiv:1106.2646 [INSPIRE].
D. Oprisa and S. Stieberger, Six gluon open superstring disk amplitude, multiple hypergeometric series and Euler-Zagier sums, hep-th/0509042 [INSPIRE].
R. Medina and L.A. Barreiro, Higher n-point amplitudes in open superstring theory, PoS IC2006 (2006) 038 [hep-th/0611349] [INSPIRE].
H. Gomes, Uso de somas harmônicas no cálculo dos coeficientes das expansões de algumas funções não elementares, undergraduate research study at Universidade Federal de Itajubá, Minas Gerais Brasil (2010).
E. Bergshoeff, M. Rakowski and E. Sezgin, Higher derivative super Yang-Mills theories, Phys. Lett. B 185 (1987) 371 [INSPIRE].
O. Andreev and A.A. Tseytlin, Partition function representation for the open superstring effective action: cancellation of Möbius infinities and derivative corrections to Born-Infeld Lagrangian, Nucl. Phys. B 311 (1988) 205 [INSPIRE].
L.A. Barreiro and R. Medina, work in progress.
M.R. Garousi, T-duality of the Riemann curvature corrections to supergravity, arXiv:1208.4459 [INSPIRE].
D.J. Gross and J.H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B 291 (1987) 41 [INSPIRE].
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ArXiv ePrint: 1208.6066
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Barreiro, L.A., Medina, R. Revisiting the S-matrix approach to the open superstring low energy effective lagrangian. J. High Energ. Phys. 2012, 108 (2012). https://doi.org/10.1007/JHEP10(2012)108
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DOI: https://doi.org/10.1007/JHEP10(2012)108