Abstract
Aimed to a deeper comprehension of a manifestly T-dual invariant formulation of string theory, in this paper a detailed comparison between the non-covariant action proposed by Tseytlin and the covariant one proposed by Hull is done. These are obtained by making both the string coordinates and their duals explicitly appear, on the same footing, in the world-sheet action, so “doubling” the string coordinates along the compact dimensions. After a discussion on the nature of the constraints in both the models and the relative quantization, it results that the string coordinates and their duals behave like “non-commuting” phase space coordinates but their expressions in terms of Fourier modes generate the oscillator algebra of the standard bosonic string. A proof of the equivalence of the two formulations is given. Furthermore, open-string solutions are also discussed.
Article PDF
Similar content being viewed by others
References
J. Maharana, The Worldsheet Perspective of T-duality Symmetry in String Theory, Int. J. Mod. Phys. A 28 (2013) 1330011 [arXiv:1302.1719] [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, 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 D.C. Thompson, Duality Symmetric String and M-theory, arXiv:1306.2643 [INSPIRE].
S. Groot Nibbelink and P. Patalong, A Lorentz invariant doubled worldsheet theory, Phys. Rev. D 87 (2013) 041902 [arXiv:1207.6110] [INSPIRE].
D.S. Berman, N.B. Copland and D.C. Thompson, Background Field Equations for the Duality Symmetric String, Nucl. Phys. B 791 (2008) 175 [arXiv:0708.2267] [INSPIRE].
D.S. Berman and D.C. Thompson, Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions, Phys. Lett. B 662 (2008) 279 [arXiv:0712.1121] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
W. Siegel, Manifest Lorentz Invariance Sometimes Requires Nonlinearity, Nucl. Phys. B 238 (1984) 307 [INSPIRE].
A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].
A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].
D. Lüst, T-duality and closed string non-commutative (doubled) geometry, JHEP 12 (2010) 084 [arXiv:1010.1361] [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.M. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, On Lorentz invariant actions for chiral p forms, Phys. Rev. D 55 (1997) 6292 [hep-th/9611100] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, Space-time symmetries in duality symmetric models, Leuven Notes in Math. and Theor. Phys. 6 167 [hep-th/9509052] [INSPIRE].
S. Groot Nibbelink, F. Kurz and P. Patalong, Renormalization of a Lorentz invariant doubled worldsheet theory, arXiv:1308.4418 [INSPIRE].
E. Hackett-Jones and G. Moutsopoulos, Quantum mechanics of the doubled torus, JHEP 10 (2006) 062 [hep-th/0605114] [INSPIRE].
D.S. Berman and N.B. Copland, The String partition function in Hull’s doubled formalism, Phys. Lett. B 649 (2007) 325 [hep-th/0701080] [INSPIRE].
N.B. Copland, A Double σ-model for Double Field Theory, JHEP 04 (2012) 044 [arXiv:1111.1828] [INSPIRE].
N.B. Copland, Connecting T-duality invariant theories, Nucl. Phys. B 854 (2012) 575 [arXiv:1106.1888] [INSPIRE].
O. Hohm, W. Siegel and B. Zwiebach, Doubled α′ -geometry, JHEP 02 (2014) 065 [arXiv:1306.2970] [INSPIRE].
D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].
C.D.A. Blair, E. Malek and A.J. Routh, An O(D,D) Invariant Hamiltonian Action for the Superstring, arXiv:1308.4829 [INSPIRE].
P. Di Vecchia, A. Liccardo, R. Marotta, I. Pesando and F. Pezzella, Wrapped magnetized branes: two alternative descriptions?, JHEP 11 (2007) 100 [arXiv:0709.4149] [INSPIRE].
R. Floreanini and R. Jackiw, Self-dual Fields as Charge Density Solitons, Phys. Rev. Lett. 59 (1987) 1873 [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
A.H. Chamseddine and J. Fröhlich, Two-dimensional Lorentz-Weyl anomaly and gravitational Chern-Simons theory, Commun. Math. Phys. 147 (1992) 549 [INSPIRE].
S.D. Avramis, J.-P. Derendinger and N. Prezas, Conformal chiral boson models on twisted doubled tori and non-geometric string vacua, Nucl. Phys. B 827 (2010) 281 [arXiv:0910.0431] [INSPIRE].
P.A.M. Dirac, Lectures on quantum mechanics, Belfer Graduate School of Science Monographs Series Number 2 (1964) [ISBN 0-486-41713-1].
C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [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: 1312.7367
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
De Angelis, L., Gionti S.J, G., Marotta, R. et al. Comparing double string theory actions. J. High Energ. Phys. 2014, 171 (2014). https://doi.org/10.1007/JHEP04(2014)171
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)171