Abstract
It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T-duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order α′ and higher, the T-duality is satisfied only for a subclass of the couplings for arbitrary base space background. They are m = 0 couplings where m is the number of \( \overset{\sim }{B} \)-field (without derivative on it). For m > 0 couplings, the base space metric must be block-diagonal and the momentum U(1) vector field in the transverse reduction must be zero. However, the derivatives of the metric and the vector field are arbitrary.
Using the assumption that the effective actions at the critical dimension are background independent, we then show that the T-duality constraint for the couplings at order α′ and for m = 0, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive α′-correction. We have also imposed the T-duality constraint on m = 1, 2, 3, 4 couplings. Because of the above restriction on the base space background in these cases, however, the T-duality can only partially fix the couplings for m > 0. This study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order α′.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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. Alvarez-Gaume and Y. Lozano, An introduction to T duality in string theory, Nucl. Phys. B Proc. Suppl. 41 (1995) 1 [hep-th/9410237] [INSPIRE].
A. Sen, O(d) × O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271 (1991) 295 [INSPIRE].
O. Hohm, A. Sen and B. Zwiebach, Heterotic effective action and duality symmetries revisited, JHEP 02 (2015) 079 [arXiv:1411.5696] [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 duality constraints, Phys. Lett. B 809 (2020) 135733 [arXiv:1907.09168] [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].
M.R. Garousi, Effective action of type II superstring theories at order α′3: NS-NS couplings, JHEP 02 (2021) 157 [arXiv:2011.02753] [INSPIRE].
M.R. Garousi, On NS-NS couplings at order α′3, Nucl. Phys. B 971 (2021) 115510 [arXiv:2012.15091] [INSPIRE].
M.R. Garousi, Higher-derivative field redefinitions in the presence of boundary, Eur. Phys. J. C 82 (2022) 645 [arXiv:2111.10987] [INSPIRE].
M.R. Garousi, Effective action of string theory at order α′ in the presence of boundary, Eur. Phys. J. C 81 (2021) 1149 [arXiv:2103.13682] [INSPIRE].
M.R. Garousi, Background independence of effective actions at critical dimension, Phys. Rev. D 105 (2022) 106021 [arXiv:2201.00588] [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 sigma models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
N. Kaloper and K.A. Meissner, Duality beyond the first loop, Phys. Rev. D 56 (1997) 7940 [hep-th/9705193] [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].
D. Marques and C.A. Nunez, T-duality and α′-corrections, JHEP 10 (2015) 084 [arXiv:1507.00652] [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].
Y. Akou and M.R. Garousi, Surface terms in effective action of O-plane at order α′2, Eur. Phys. J. C 81 (2021) 201 [arXiv:2012.13264] [INSPIRE].
M. Mashhadi and M.R. Garousi, O-plane couplings at order α′2: one R-R field strength, JHEP 06 (2020) 171 [arXiv:2003.05359] [INSPIRE].
S. Karimi and M.R. Garousi, α′-corrections to DBI action via T-duality constraint, Nucl. Phys. B 939 (2019) 485 [arXiv:1809.10377] [INSPIRE].
M.R. Garousi and S. Karimi, Couplings of order six in the gauge field strength and the second fundamental form on Dp-branes at order α′2, Phys. Rev. D 106 (2022) 066016 [arXiv:2207.09834] [INSPIRE].
M.R. Garousi, A. Ghodsi, T. Houri and G. Jafari, T-duality of D-brane action at order α′ in bosonic string theory, JHEP 10 (2013) 103 [arXiv:1308.4609] [INSPIRE].
R.G. Leigh, Dirac-Born-Infeld action from Dirichlet sigma model, Mod. Phys. Lett. A 4 (1989) 2767 [INSPIRE].
C. Bachas, D-brane dynamics, Phys. Lett. B 374 (1996) 37 [hep-th/9511043] [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].
J. Maharana and J.H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys. B 390 (1993) 3 [hep-th/9207016] [INSPIRE].
S. Corley, D.A. Lowe and S. Ramgoolam, Einstein-Hilbert action on the brane for the bulk graviton, JHEP 07 (2001) 030 [hep-th/0106067] [INSPIRE].
J. Polchinski, Tasi lectures on D-branes, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): fields, strings, and duality, (1996), p. 293 [hep-th/9611050] [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].
F. Ardalan, H. Arfaei, M.R. Garousi and A. Ghodsi, Gravity on noncommutative D-branes, Int. J. Mod. Phys. A 18 (2003) 1051 [hep-th/0204117] [INSPIRE].
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].
M.R. Garousi and R.C. Myers, Superstring scattering from D-branes, Nucl. Phys. B 475 (1996) 193 [hep-th/9603194] [INSPIRE].
N. Wyllard, Derivative corrections to D-brane actions with constant background fields, Nucl. Phys. B 598 (2001) 247 [hep-th/0008125] [INSPIRE].
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: 2210.03972
Rights and permissions
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.
About this article
Cite this article
Hosseini, M.R., Garousi, M.R. T-duality of D-brane versus O-plane actions. J. High Energ. Phys. 2023, 12 (2023). https://doi.org/10.1007/JHEP01(2023)012
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2023)012