Abstract
We recently introduced a T-duality covariant mechanism to compute all-order higher-derivative interactions in the heterotic string. Here we extend the formalism to account for a two-parameter family of corrections that also include the bosonic string and HSZ theory. We use our result to compute the full second order Double Field Theory (DFT) for generic values of the parameters, including the generalized Green-Schwarz transformation and its invariant action.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [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].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double field theory: a pedagogical review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
D.S. Berman and D.C. Thompson, Duality symmetric string and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].
O. Hohm, D. Lüst and B. Zwiebach, The spacetime of double field theory: review, remarks, and outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].
D.S. Berman and C.D.A. Blair, The geometry, branes and applications of exceptional field theory, Int. J. Mod. Phys. A 35 (2020) 2030014 [arXiv:2006.09777] [INSPIRE].
K.A. Meissner, Symmetries of higher order string gravity actions, Phys. Lett. B 392 (1997) 298 [hep-th/9610131] [INSPIRE].
O. Hohm and B. Zwiebach, T-duality constraints on higher derivatives revisited, JHEP 04 (2016) 101 [arXiv:1510.00005] [INSPIRE].
E. Bergshoeff, B. Janssen and T. Ortín, 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, Duality constraints on effective actions, Phys. Rept. 702 (2017) 1 [arXiv:1702.00191] [INSPIRE].
M.R. Garousi, O(D, D)-constraint on D-dimensional effective actions, Phys. Rev. D 98 (2018) 066008 [arXiv:1805.08977] [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].
H. Razaghian and M.R. Garousi, T-duality invariant effective actions at orders α′, α′2, JHEP 02 (2018) 056 [arXiv:1709.01291] [INSPIRE].
C. Eloy, O. Hohm and H. Samtleben, Duality invariance and higher derivatives, Phys. Rev. D 101 (2020) 126018 [arXiv:2004.13140] [INSPIRE].
C. Eloy, O. Hohm and H. Samtleben, Green-Schwarz mechanism for string dualities, Phys. Rev. Lett. 124 (2020) 091601 [arXiv:1912.01700] [INSPIRE].
H. Godazgar and M. Godazgar, Duality completion of higher derivative corrections, JHEP 09 (2013) 140 [arXiv:1306.4918] [INSPIRE].
R. Bonezzi, F. Diaz-Jaramillo and O. Hohm, Old dualities and new anomalies, Phys. Rev. D 102 (2020) 126002 [arXiv:2008.06420] [INSPIRE].
O.A. Bedoya, D. Marques and C. Núñez, Heterotic α′-corrections in double field theory, JHEP 12 (2014) 074 [arXiv:1407.0365] [INSPIRE].
A. Coimbra, R. Minasian, H. Triendl and D. Waldram, Generalised geometry for string corrections, JHEP 11 (2014) 160 [arXiv:1407.7542] [INSPIRE].
K. Lee, Quadratic α′-corrections to heterotic double field theory, Nucl. Phys. B 899 (2015) 594 [arXiv:1504.00149] [INSPIRE].
A. Coimbra, Higher curvature Bianchi identities, generalised geometry and L∞ algebras, Phys. Rev. D 100 (2019) 106001 [arXiv:1907.09501] [INSPIRE].
O. Hohm, W. Siegel and B. Zwiebach, Doubled α′-geometry, JHEP 02 (2014) 065 [arXiv:1306.2970] [INSPIRE].
O. Hohm and B. Zwiebach, Green-Schwarz mechanism and α′-deformed Courant brackets, JHEP 01 (2015) 012 [arXiv:1407.0708] [INSPIRE].
O. Hohm and B. Zwiebach, Double metric, generalized metric, and α′-deformed double field theory, Phys. Rev. D 93 (2016) 064035 [arXiv:1509.02930] [INSPIRE].
U. Naseer and B. Zwiebach, Three-point functions in duality-invariant higher-derivative gravity, JHEP 03 (2016) 147 [arXiv:1602.01101] [INSPIRE].
E. Lescano and D. Marques, Second order higher-derivative corrections in double field theory, JHEP 06 (2017) 104 [arXiv:1611.05031] [INSPIRE].
O. Hohm and B. Zwiebach, Double field theory at order α′, JHEP 11 (2014) 075 [arXiv:1407.3803] [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. Núñez, The odd story of α′-corrections, JHEP 04 (2017) 078 [arXiv:1702.05489] [INSPIRE].
O. Hohm, Background independence and duality invariance in string theory, Phys. Rev. Lett. 118 (2017) 131601 [arXiv:1612.03966] [INSPIRE].
O. Hohm, Background independent double field theory at order α′: metric vs. frame-like geometry, Phys. Rev. D 95 (2017) 066018 [arXiv:1612.06453] [INSPIRE].
W.H. Baron, E. Lescano and D. Marqués, The generalized Bergshoeff-de Roo identification, JHEP 11 (2018) 160 [arXiv:1810.01427] [INSPIRE].
O. Hohm and S.K. Kwak, Double field theory formulation of heterotic strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].
O. Hohm, A. Sen and B. Zwiebach, Heterotic effective action and duality symmetries revisited, JHEP 02 (2015) 079 [arXiv:1411.5696] [INSPIRE].
E. Bergshoeff and M. de Roo, Supersymmetric Chern-Simons terms in ten-dimensions, Phys. Lett. B 218 (1989) 210 [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].
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].
M. Graña and D. Marques, Gauged double field theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
O. Hohm and S.K. Kwak, Frame-like geometry of double field theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring double field theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as generalised geometry I: type II theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].
G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of double field theory, JHEP 11 (2011) 052 [Erratum ibid. 11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
D. Geissbuhler, Double field theory and N = 4 gauged supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
G. Dibitetto, J.J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].
K. Peeters, Introducing Cadabra: a symbolic computer algebra system for field theory problems, hep-th/0701238 [INSPIRE].
O. Hohm and B. Zwiebach, Large gauge transformations in double field theory, JHEP 02 (2013) 075 [arXiv:1207.4198] [INSPIRE].
J.-H. Park, Comments on double field theory and diffeomorphisms, JHEP 06 (2013) 098 [arXiv:1304.5946] [INSPIRE].
D.S. Berman, M. Cederwall and M.J. Perry, Global aspects of double geometry, JHEP 09 (2014) 066 [arXiv:1401.1311] [INSPIRE].
C.M. Hull, Finite gauge transformations and geometry in double field theory, JHEP 04 (2015) 109 [arXiv:1406.7794] [INSPIRE].
U. Naseer, A note on large gauge transformations in double field theory, JHEP 06 (2015) 002 [arXiv:1504.05913] [INSPIRE].
S.-J. Rey and Y. Sakatani, Finite transformations in doubled and exceptional space, arXiv:1510.06735 [INSPIRE].
R. Borsato, A. Vilar López and L. Wulff, The first α′-correction to homogeneous Yang-Baxter deformations using O(d, d), JHEP 07 (2020) 103 [arXiv:2003.05867] [INSPIRE].
F. Hassler and T. Rochais, α′-corrected Poisson-Lie T-duality, Fortsch. Phys. 68 (2020) 2000063 [arXiv:2007.07897] [INSPIRE].
R. Borsato and L. Wulff, Quantum correction to generalized T dualities, Phys. Rev. Lett. 125 (2020) 201603 [arXiv:2007.07902] [INSPIRE].
T. Codina and D. Marques, Generalized dualities and higher derivatives, JHEP 10 (2020) 002 [arXiv:2007.09494] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Order α′ (two loop) equivalence of the string equations of motion and the sigma 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].
D.J. Gross and J.H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B 291 (1987) 41 [INSPIRE].
S. Hronek and L. Wulff, Relaxing unimodularity for Yang-Baxter deformed strings, JHEP 10 (2020) 065 [arXiv:2007.15663] [INSPIRE].
O. Hohm and B. Zwiebach, Non-perturbative de Sitter vacua via α′ corrections, Int. J. Mod. Phys. D 28 (2019) 1943002 [arXiv:1905.06583] [INSPIRE].
O. Hohm and B. Zwiebach, Duality invariant cosmology to all orders in α′, Phys. Rev. D 100 (2019) 126011 [arXiv:1905.06963] [INSPIRE].
T. Ortín, O(n, n) invariance and Wald entropy formula in the heterotic superstring effective action at first order in α′, arXiv:2005.14618 [INSPIRE].
Z. Elgood and T. Ortín, T duality and Wald entropy formula in the heterotic superstring effective action at first-order in α′, JHEP 10 (2020) 097 [arXiv:2005.11272] [INSPIRE].
P.A. Cano, P. Meessen, T. Ortín and P.F. Ramírez, α′-corrected black holes in string theory, JHEP 05 (2018) 110 [arXiv:1803.01919] [INSPIRE].
J.D. Edelstein, K. Sfetsos, J.A. Sierra-Garcia and A. Vilar López, T-duality equivalences beyond string theory, JHEP 05 (2019) 082 [arXiv:1903.05554] [INSPIRE].
J.D. Edelstein, K. Sfetsos, J.A. Sierra-Garcia and A. Vilar López, T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm, JHEP 06 (2018) 142 [arXiv:1803.04517] [INSPIRE].
C. Krishnan, De Sitter, α′-corrections & duality invariant cosmology, JCAP 10 (2019) 009 [arXiv:1906.09257] [INSPIRE].
P. Wang, H. Wu, H. Yang and S. Ying, Non-singular string cosmology via α′ corrections, JHEP 10 (2019) 263 [arXiv:1909.00830] [INSPIRE].
P. Wang, H. Wu, H. Yang and S. Ying, Construct α′ corrected or loop corrected solutions without curvature singularities, JHEP 01 (2020) 164 [arXiv:1910.05808] [INSPIRE].
H. Bernardo, R. Brandenberger and G. Franzmann, O(d, d) covariant string cosmology to all orders in α′, JHEP 02 (2020) 178 [arXiv:1911.00088] [INSPIRE].
H. Bernardo and G. Franzmann, α′-cosmology: solutions and stability analysis, JHEP 05 (2020) 073 [arXiv:2002.09856] [INSPIRE].
H. Bernardo, R. Brandenberger and G. Franzmann, String cosmology backgrounds from classical string geometry, arXiv:2005.08324 [INSPIRE].
H. Bernardo, R. Brandenberger and G. Franzmann, Solution of the size and horizon problems from classical string geometry, JHEP 10 (2020) 155 [arXiv:2007.14096] [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: 2009.07291
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
Baron, W., Marques, D. The generalized Bergshoeff-de Roo identification. Part II. J. High Energ. Phys. 2021, 171 (2021). https://doi.org/10.1007/JHEP01(2021)171
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)171