Abstract
It is known that the anomalous Chern-Simons (CS) coupling of Op-plane is not consistent with the T-duality transformations. Compatibility of this coupling with the T-duality requires the inclusion of couplings involving one R-R field strength. In this paper we find such couplings at order α′2. By requiring the R-R and NS-NS gauge invariances, we first find all independent couplings at order α′2. There are 1, 6, 28, 20, 19, 2 couplings corresponding to the R-R field strengths F (p−4), F (p−2), F (p), F (p+2), F (p+4) and F (p+6), respectively. We then impose the T-duality constraint on these couplings and on the CS coupling C (p−3) ∧ R ∧ R at order α′2 to fix their corresponding coefficients. The T-duality constraint fixes all coefficients in terms of the CS coefficient. They are fully consistent with the partial couplings that have been already found in the literature by the S-matrix method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski, TASI lectures on D-branes, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings and Duality, Boulder U.S.A. (1996), pg. 293 [hep-th/9611050] [INSPIRE].
K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, Cambridge U.K. (2006).
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, An Introduction to T duality in string theory, hep-th/9410237 [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].
M.R. Garousi, Duality constraints on effective actions, Phys. Rept. 702 (2017) 1 [arXiv:1702.00191] [INSPIRE].
T.H. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
T.H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
A.A. Tseytlin, Duality and dilaton, Mod. Phys. Lett. A 6 (1991) 1721 [INSPIRE].
E. Bergshoeff, B. Janssen and T. Ort́ın, Solution generating transformations and the string effective action, Class. Quant. Grav. 13 (1996) 321 [hep-th/9506156] [INSPIRE].
N. Kaloper and K.A. Meissner, Duality beyond the first loop, Phys. Rev. D 56 (1997) 7940 [hep-th/9705193] [INSPIRE].
M.R. Garousi, Four-derivative couplings via the T -duality invariance constraint, Phys. Rev. D 99 (2019) 126005 [arXiv:1904.11282] [INSPIRE].
M.R. Garousi, Effective action of bosonic string theory at order α′2 , Eur. Phys. J. C 79 (2019) 827 [arXiv:1907.06500] [INSPIRE].
M.R. Garousi, Surface terms in the effective actions via T-duality constraint, arXiv:1907.09168 [INSPIRE].
M.R. Garousi, T-duality constraint on RR couplings, arXiv:1908.06627 [INSPIRE].
J.W. York, Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
H. Razaghian and M.R. Garousi, R4 terms in supergravities via T-duality constraint, Phys. Rev. D 97 (2018) 106013 [arXiv:1801.06834] [INSPIRE].
J. Scherk and J.H. Schwarz, Dual Models and the Geometry of Space-Time, Phys. Lett. B 52 (1974) 347 [INSPIRE].
T. Yoneya, Connection of Dual Models to Electrodynamics and Gravidynamics, Prog. Theor. Phys. 51 (1974) 1907 [INSPIRE].
C.G. Callan Jr., E.J. Martinec, M.J. Perry and D. Friedan, Strings in Background Fields, Nucl. Phys. B 262 (1985) 593 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Effective Field Theory from Quantized Strings, Phys. Lett. B 158 (1985) 316 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Effective Action Approach to Superstring Theory, Phys. Lett. B 160 (1985) 69 [INSPIRE].
J. Gates, S. James and H. Nishino, New D = 10, N = 1 Superspace Supergravity and Local Symmetries of Superstrings, Phys. Lett. B 173 (1986) 46 [INSPIRE].
J. Gates, S.J. and H. Nishino, Manifestly Supersymmetric O(α ) Superstring Corrections in New D = 10, N = 1 Supergravity Yang-Mills Theory, Phys. Lett. B 173 (1986) 52 [INSPIRE].
E. Bergshoeff, A. Salam and E. Sezgin, Supersymmetric R2 Actions, Conformal Invariance and Lorentz Chern-Simons Term in Six-dimensions and Ten-dimensions, Nucl. Phys. B 279 (1987) 659 [INSPIRE].
E.A. Bergshoeff and M. de Roo, The Quartic Effective Action of the Heterotic String and Supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
D. Robbins and Z. Wang, Higher Derivative Corrections to O-plane Actions: NS-NS Sector, JHEP 05 (2014) 072 [arXiv:1401.4180] [INSPIRE].
M.R. Garousi, T-duality of O-plane action at order α′2 , Phys. Lett. B 747 (2015) 53 [arXiv:1412.8131] [INSPIRE].
M.B. Green, J.A. Harvey and G.W. Moore, I-brane inflow and anomalous couplings on D-branes, Class. Quant. Grav. 14 (1997) 47 [hep-th/9605033] [INSPIRE].
Y.-K.E. Cheung and Z. Yin, Anomalies, branes and currents, Nucl. Phys. B 517 (1998) 69 [hep-th/9710206] [INSPIRE].
R. Minasian and G.W. Moore, K theory and Ramond-Ramond charge, JHEP 11 (1997) 002 [hep-th/9710230] [INSPIRE].
B. Craps and F. Roose, Anomalous D-brane and orientifold couplings from the boundary state, Phys. Lett. B 445 (1998) 150 [hep-th/9808074] [INSPIRE].
J.F. Morales, C.A. Scrucca and M. Serone, Anomalous couplings for D-branes and O-planes, Nucl. Phys. B 552 (1999) 291 [hep-th/9812071] [INSPIRE].
B. Stefański Jr., Gravitational couplings of D-branes and O-planes, Nucl. Phys. B 548 (1999) 275 [hep-th/9812088] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
K. Becker and A. Bergman, Geometric Aspects of D-branes and T-duality, JHEP 11 (2009) 067 [arXiv:0908.2249] [INSPIRE].
K. Becker, G. Guo and D. Robbins, Higher Derivative Brane Couplings from T-duality, JHEP 09 (2010) 029 [arXiv:1007.0441] [INSPIRE].
M.R. Garousi, T-duality of anomalous Chern-Simons couplings, Nucl. Phys. B 852 (2011) 320 [arXiv:1007.2118] [INSPIRE].
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].
K. Becker, G. Guo and D. Robbins, Four-Derivative Brane Couplings from String Amplitudes, JHEP 12 (2011) 050 [arXiv:1110.3831] [INSPIRE].
M.R. Garousi, Ramond-Ramond field strength couplings on D-branes, JHEP 03 (2010) 126 [arXiv:1002.0903] [INSPIRE].
M.R. Garousi, Superstring scattering from O-planes, Nucl. Phys. B 765 (2007) 166 [hep-th/0611173] [INSPIRE].
T. Nutma, xTras: A field-theory inspired xAct package for mathematica, Comput. Phys. Commun. 185 (2014) 1719 [arXiv:1308.3493] [INSPIRE].
M.R. Garousi and H. Razaghian, Minimal independent couplings at order α′2 , Phys. Rev. D 100 (2019) 106007 [arXiv:1905.10800] [INSPIRE].
K.B. Velni and M.R. Garousi, Ramond-Ramond S-matrix elements from the T-dual Ward identity, Phys. Rev. D 89 (2014) 106002 [arXiv:1312.0213] [INSPIRE].
P. Meessen and T. Ortín, An SL(2, ℤ) multiplet of nine-dimensional type-II supergravity theories, Nucl. Phys. B 541 (1999) 195 [hep-th/9806120] [INSPIRE].
J. Maharana and J.H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys. B 390 (1993) 3 [hep-th/9207016] [INSPIRE].
K. Becker, M. Becker, D. Robbins and N. Su, Three-Point Disc Amplitudes in the RNS Formalism, Nucl. Phys. B 907 (2016) 360 [arXiv:1601.02660] [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2003.05359
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Mashhadi, M., Garousi, M.R. O-plane couplings at order α′2: one R-R field strength. J. High Energ. Phys. 2020, 171 (2020). https://doi.org/10.1007/JHEP06(2020)171
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)171