Abstract
We revisit T-duality transformations for the open string via Buscher’s procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider T-duality along directions with Neumann as well as Dirichlet boundary conditions, and we include collective T-duality along multiple directions.
We illustrate this formalism with the example of the three-torus with H-flux and its T-dual backgrounds, and we discuss global properties of open-string boundary conditions on such spaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
S. Kachru, M.B. Schulz, P.K. Tripathy and S.P. Trivedi, New supersymmetric string compactifications, JHEP 03 (2003) 061 [hep-th/0211182] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Generalized Flux Vacua, JHEP 02 (2007) 095 [hep-th/0607015] [INSPIRE].
V. Mathai and J.M. Rosenberg, T duality for torus bundles with H fluxes via noncommutative topology, Commun. Math. Phys. 253 (2004) 705 [hep-th/0401168] [INSPIRE].
V. Mathai and J.M. Rosenberg, On mysteriously missing T-duals, H-flux and the T-duality group, in Differential geometry and physics. Proceedings, 23rd International Conference, Tianjin, China, August 20-26, 2005, pp. 350-358, hep-th/0409073 [INSPIRE].
D. Lüst, T-duality and closed string non-commutative (doubled) geometry, JHEP 12 (2010) 084 [arXiv:1010.1361] [INSPIRE].
C. Condeescu, I. Florakis and D. Lüst, Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory, JHEP 04 (2012) 121 [arXiv:1202.6366] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-Geometric Fluxes in Supergravity and Double Field Theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].
D. Andriot, M. Larfors, D. Lüst and P. Patalong, (Non-)commutative closed string on T-dual toroidal backgrounds, JHEP 06 (2013) 021 [arXiv:1211.6437] [INSPIRE].
C.D.A. Blair, Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds, JHEP 06 (2015) 091 [arXiv:1405.2283] [INSPIRE].
P. Bouwknegt, K. Hannabuss and V. Mathai, Nonassociative tori and applications to T-duality, Commun. Math. Phys. 264 (2006) 41 [hep-th/0412092] [INSPIRE].
I. Ellwood and A. Hashimoto, Effective descriptions of branes on non-geometric tori, JHEP 12 (2006) 025 [hep-th/0607135] [INSPIRE].
R. Blumenhagen and E. Plauschinn, Nonassociative Gravity in String Theory?, J. Phys. A 44 (2011) 015401 [arXiv:1010.1263] [INSPIRE].
R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].
E. Plauschinn, Non-geometric fluxes and non-associative geometry, PoS(CORFU2011)061 [arXiv:1203.6203] [INSPIRE].
D. Mylonas, P. Schupp and R.J. Szabo, Membrane sigma-models and Quantization of Non-Geometric Flux Backgrounds, JHEP 09 (2012) 012 [arXiv:1207.0926] [INSPIRE].
I. Bakas and D. Lüst, 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua, JHEP 01 (2014) 171 [arXiv:1309.3172] [INSPIRE].
D. Mylonas, P. Schupp and R.J. Szabo, Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics, J. Math. Phys. 55 (2014) 122301 [arXiv:1312.1621] [INSPIRE].
A. Chatzistavrakidis, L. Jonke and O. Lechtenfeld, Sigma-models for genuinely non-geometric backgrounds, JHEP 11 (2015) 182 [arXiv:1505.05457] [INSPIRE].
R.J. Szabo, Higher Quantum Geometry and Non-Geometric String Theory, in 17th Hellenic School and Workshops on Elementary Particle Physics and Gravity (CORFU2017) Corfu, Greece, September 2-28, 2017, 2018, arXiv:1803.08861 [INSPIRE].
G. Aldazabal, P.G. Camara, A. Font and L.E. Ibáñez, More dual fluxes and moduli fixing, JHEP 05 (2006) 070 [hep-th/0602089] [INSPIRE].
G. Villadoro and F. Zwirner, D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications, JHEP 03 (2006) 087 [hep-th/0602120] [INSPIRE].
A. Micu, E. Palti and G. Tasinato, Towards Minkowski Vacua in Type II String Compactifications, JHEP 03 (2007) 104 [hep-th/0701173] [INSPIRE].
A. Font, A. Guarino and J.M. Moreno, Algebras and non-geometric flux vacua, JHEP 12 (2008) 050 [arXiv:0809.3748] [INSPIRE].
C. Caviezel, T. Wrase and M. Zagermann, Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds, JHEP 04 (2010) 011 [arXiv:0912.3287] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Charting the landscape of N = 4 flux compactifications, JHEP 03 (2011) 137 [arXiv:1102.0239] [INSPIRE].
F. Hassler, D. Lüst and S. Massai, On Inflation and de Sitter in Non-Geometric String Backgrounds, Fortsch. Phys. 65 (2017) 1700062 [arXiv:1405.2325] [INSPIRE].
R. Blumenhagen et al., A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory, Nucl. Phys. B 897 (2015) 500 [arXiv:1503.07634] [INSPIRE].
A. Lawrence, M.B. Schulz and B. Wecht, D-branes in nongeometric backgrounds, JHEP 07 (2006) 038 [hep-th/0602025] [INSPIRE].
C. Albertsson, T. Kimura and R.A. Reid-Edwards, D-branes and doubled geometry, JHEP 04 (2009) 113 [arXiv:0806.1783] [INSPIRE].
T.H. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
E. Alvarez, J.L.F. Barbon and J. Borlaf, T duality for open strings, Nucl. Phys. B 479 (1996) 218 [hep-th/9603089] [INSPIRE].
H. Dorn and H.J. Otto, On T duality for open strings in general Abelian and nonAbelian gauge field backgrounds, Phys. Lett. B 381 (1996) 81 [hep-th/9603186] [INSPIRE].
H. Dorn and H.J. Otto, Remarks on T duality for open strings, Nucl. Phys. Proc. Suppl. B 56 (1997) 30 [hep-th/9702018] [INSPIRE].
S. Förste, A.A. Kehagias and S. Schwager, NonAbelian duality for open strings, Nucl. Phys. B 478 (1996) 141 [hep-th/9604013] [INSPIRE].
S. Förste, A.A. Kehagias and S. Schwager, NonAbelian T duality for open strings, Nucl. Phys. Proc. Suppl. B 56 (1997) 36 [hep-th/9610062] [INSPIRE].
S. Förste, A.A. Kehagias and S. Schwager, T duality for open strings with respect to nonAbelian isometries, in Gauge theories, applied supersymmetry and quantum gravity. Proceedings, 2nd Conference, London, U.K., July 5-10, 1996, pp. 271-278, hep-th/9611060 [INSPIRE].
C. Albertsson, U. Lindström and M. Zabzine, T-duality for the sigma model with boundaries, JHEP 12 (2004) 056 [hep-th/0410217] [INSPIRE].
J. Borlaf and Y. Lozano, Aspects of T duality in open strings, Nucl. Phys. B 480 (1996) 239 [hep-th/9607051] [INSPIRE].
Y. Lozano, Duality and canonical transformations, Mod. Phys. Lett. A 11 (1996) 2893 [hep-th/9610024] [INSPIRE].
A.A. Tseytlin, Selfduality of Born-Infeld action and Dirichlet three-brane of type IIB superstring theory, Nucl. Phys. B 469 (1996) 51 [hep-th/9602064] [INSPIRE].
E. Bergshoeff and M. De Roo, D-branes and T duality, Phys. Lett. B 380 (1996) 265 [hep-th/9603123] [INSPIRE].
M.B. Green, C.M. Hull and P.K. Townsend, D-brane Wess-Zumino actions, t duality and the cosmological constant, Phys. Lett. B 382 (1996) 65 [hep-th/9604119] [INSPIRE].
S. Kawai and Y. Sugawara, D-branes in T-fold conformal field theory, JHEP 02 (2008) 027 [arXiv:0709.0257] [INSPIRE].
P. Grange and R. Minasian, Tachyon condensation and D-branes in generalized geometries, Nucl. Phys. B 741 (2006) 199 [hep-th/0512185] [INSPIRE].
C. Klimčík and P. Ševera, Poisson Lie T duality: Open strings and D-branes, Phys. Lett. B 376 (1996) 82 [hep-th/9512124] [INSPIRE].
C. Albertsson and R.A. Reid-Edwards, Worldsheet boundary conditions in Poisson-Lie T-duality, JHEP 03 (2007) 004 [hep-th/0606024] [INSPIRE].
L. Davidović, Open string T-duality in a weakly curved background, Eur. Phys. J. C 76 (2016) 660 [arXiv:1603.06411] [INSPIRE].
B. Sazdović, From geometry to non-geometry via T-duality, Chin. Phys. C 42 (2018) 083106 [arXiv:1606.01938] [INSPIRE].
B. Sazdović, Open string T-duality in double space, Eur. Phys. J. C 77 (2017) 634 [arXiv:1704.01163] [INSPIRE].
S. Cappell, D. DeTurck, H. Gluck and E.Y. Miller, Cohomology of Harmonic Forms on Riemannian Manifolds With Boundary, math/0508372 [INSPIRE].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
A. Giveon and M. Roček, On nonAbelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé, J.L.F. Barbon and Y. Lozano, Some global aspects of duality in string theory, Nucl. Phys. B 415 (1994) 71 [hep-th/9309039] [INSPIRE].
E. Plauschinn, On T-duality transformations for the three-sphere, Nucl. Phys. B 893 (2015) 257 [arXiv:1408.1715] [INSPIRE].
T.H. Buscher, Path integral derivation of quantum duality in nonlinear sigma-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
E. Plauschinn, T-duality revisited, JHEP 01 (2014) 131 [arXiv:1310.4194] [INSPIRE].
D.S. Freed and E. Witten, Anomalies in string theory with D-branes, Asian J. Math. 3 (1999) 819 [hep-th/9907189] [INSPIRE].
P.G. Camara, A. Font and L.E. Ibáñez, Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold, JHEP 09 (2005) 013 [hep-th/0506066] [INSPIRE].
O. Loaiza-Brito, Freed-Witten anomaly in general flux compactification, Phys. Rev. D 76 (2007) 106015 [hep-th/0612088] [INSPIRE].
G. Aldazabal, P.G. Camara and J.A. Rosabal, Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications, Nucl. Phys. B 814 (2009) 21 [arXiv:0811.2900] [INSPIRE].
G. Aldazabal, D. Marques, C. Núñez and J.A. Rosabal, On type IIB moduli stabilization and N = 4, 8 supergravities, Nucl. Phys. B 849 (2011) 80 [arXiv:1101.5954] [INSPIRE].
X.C. de la Ossa and F. Quevedo, Duality symmetries from nonAbelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].
K. Sfetsos, Gauged WZW models and nonAbelian duality, Phys. Rev. D 50 (1994) 2784 [hep-th/9402031] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, On nonAbelian duality, Nucl. Phys. B 424 (1994) 155 [hep-th/9403155] [INSPIRE].
Y. Lozano, NonAbelian duality and canonical transformations, Phys. Lett. B 355 (1995) 165 [hep-th/9503045] [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: 1806.01308
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Cordonier-Tello, F., Lüst, D. & Plauschinn, E. Open-string T-duality and applications to non-geometric backgrounds. J. High Energ. Phys. 2018, 198 (2018). https://doi.org/10.1007/JHEP08(2018)198
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)198