Abstract
We use compatibility of the D-dimensional effective actions for diagonal metric and for dilaton with the T-duality when theory is compactified on a circle, to find the D-dimensional couplings of curvatures and dilaton as well as the higher derivative corrections to the (D − 1)-dimensional Buscher rules at orders α′ and α′2. We observe that the T-duality constraint on the effective actions fixes the covariant effective actions at each order of α′ up to field redefinitions and up to an overall factor. Inspired by these results, we speculate that the D-dimensional effective actions at any order of α′ must be consistent with the standard Buscher rules provided that one uses covariant field redefinitions in the corresponding reduced (D − 1)-dimensional effective actions. This constraint may be used to find effective actions at all higher orders of α′.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S.J. Gates Jr. and H. Nishino, New D = 10, N = 1 Superspace Supergravity and Local Symmetries of Superstrings, Phys. Lett. B 173 (1986) 46 [INSPIRE].
S.J. Gates Jr. 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 R 2 Actions, Conformal Invariance and Lorentz Chern-Simons Term in Six-dimensions and Ten-dimensions, Nucl. Phys. B 279 (1987) 659 [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
W. Siegel, Manifest duality in low-energy superstrings, hep-th/9308133 [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].
S. Ferrara, D. Lüst, A.D. Shapere and S. Theisen, Modular Invariance in Supersymmetric Field Theories, Phys. Lett. B 225 (1989) 363 [INSPIRE].
A. Font, L.E. Ibáñez, D. Lüst and F. Quevedo, Strong-weak coupling duality and non-perturbative effects in string theory, Phys. Lett. B 249 (1990) 35 [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. 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].
N. Kaloper and K.A. Meissner, Duality beyond the first loop, Phys. Rev. D 56 (1997) 7940 [hep-th/9705193] [INSPIRE].
H. Godazgar and M. Godazgar, Duality completion of higher derivative corrections, JHEP 09 (2013) 140 [arXiv:1306.4918] [INSPIRE].
M.R. Garousi, T-duality of α ′ -correction to DBI action at all orders of gauge field, Nucl. Phys. B 909 (2016) 1 [arXiv:1512.09225] [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.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].
M.B. Green and J.H. Schwarz, Anomaly Cancellation in Supersymmetric D = 10 Gauge Theory and Superstring Theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].
K.A. Meissner, Symmetries of higher order string gravity actions, Phys. Lett. B 392 (1997) 298 [hep-th/9610131] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Order α ′ (Two-Loop) Equivalence of the String Equations of Motion and the σ-model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor, Nucl. Phys. B 293 (1987) 385 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Curvature Cubed Terms in String Theory Effective Actions, Phys. Lett. B 185 (1987) 52 [INSPIRE].
M.C. Bento, O. Bertolami, A.B. Henriques and J.C. Romao, Order α ′2 Terms in the Gravitational Sector of String Effective Actions With the Inclusion of the Dilaton Field, Phys. Lett. B 218 (1989) 162 [INSPIRE].
M.C. Bento, O. Bertolami, A.B. Henriques and J.C. Romao, Order α ′2 Equivalence of the String Equations of Motion and the σ-Model Weyl Invariance Conditions: Dependence on the Dilaton Field, Phys. Lett. B 220 (1989) 113 [INSPIRE].
M.C. Bento, O. Bertolami and J.C. Romao, On the interdependence of the structure of string effective actions at different orders in α ′, Phys. Lett. B 252 (1990) 401 [INSPIRE].
M.C. Bento, O. Bertolami and J.C. Romao, On The Equivalence Of The String Equations Of Motion And The σ-Model Weyl Invariance Conditions At Order α ′2 : Dependence On The Dilaton Field, Int. J. Mod. Phys. A 6 (1991) 5099 [INSPIRE].
I. Jack, D.R.T. Jones and D.A. Ross, On the Relationship Between String Low-energy Effective Actions and O(α ′3) σ-Model β-functions, Nucl. Phys. B 307 (1988) 130 [INSPIRE].
D. Marques and C.A. Núñez, T-duality and α ′ -corrections, JHEP 10 (2015) 084 [arXiv:1507.00652] [INSPIRE].
W.H. Baron, J.J. Fernandez-Melgarejo, D. Marques and C.A. Núñez, The Odd story of α ′ -corrections, JHEP 04 (2017) 078 [arXiv:1702.05489] [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
ArXiv ePrint: 1709.01291
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Razaghian, H., Garousi, M.R. T-duality invariant effective actions at orders α′, α′2. J. High Energ. Phys. 2018, 56 (2018). https://doi.org/10.1007/JHEP02(2018)056
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)056