Abstract
We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of “spectator” fields in this process and also show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double. We then develop the \( \mathcal{N} \) = (0, 1) supersymmetric duality invariant formalism.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.J. Duff, Duality rotations in string theory, Nucl. Phys. B 335 (1990) 610 [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].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
C.M. Hull, Doubled geometry and T-folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].
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].
D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional form of D = 11 supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [INSPIRE].
P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double field theory: a pedagogical review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [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, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].
L. Freidel, R.G. Leigh and D. Minic, Born reciprocity in string theory and the nature of spacetime, Phys. Lett. B 730 (2014) 302 [arXiv:1307.7080] [INSPIRE].
L. Freidel, R.G. Leigh and D. Minic, Metastring theory and modular space-time, JHEP 06 (2015) 006 [arXiv:1502.08005] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Double field theory of type II strings, JHEP 09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. 54 (2003) 281 [math/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, math/0401221 [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].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as generalised geometry II: \( {E_d}_{(d)}\times {\mathbb{R}}^{+} \) and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
O. Hohm and S.K. Kwak, Massive type II in double field theory, JHEP 11 (2011) 086 [arXiv:1108.4937] [INSPIRE].
D. Geissbuhler, Double field theory and N = 4 gauged supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [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].
M. Graña and D. Marques, Gauged double field theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
D.S. Berman, E.T. Musaev, D.C. Thompson and D.C. Thompson, Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions, JHEP 10 (2012) 174 [arXiv:1208.0020] [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].
H.S. Tan, Closed string partition functions in toroidal compactifications of doubled geometries, JHEP 05 (2014) 133 [arXiv:1403.4683] [INSPIRE].
R. Floreanini and R. Jackiw, Selfdual fields as charge density solitons, Phys. Rev. Lett. 59 (1987) 1873 [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].
N.B. Copland, A double σ-model for double field theory, JHEP 04 (2012) 044 [arXiv:1111.1828] [INSPIRE].
K. Lee and J.-H. Park, Covariant action for a string in “doubled yet gauged” spacetime, Nucl. Phys. B 880 (2014) 134 [arXiv:1307.8377] [INSPIRE].
A. Betz, R. Blumenhagen, D. Lüst and F. Rennecke, A note on the CFT origin of the strong constraint of DFT, JHEP 05 (2014) 044 [arXiv:1402.1686] [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].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
S. Groot Nibbelink and P. Patalong, A Lorentz invariant doubled world-sheet theory, Phys. Rev. D 87 (2013) 041902 [arXiv:1207.6110] [INSPIRE].
S. Groot Nibbelink, F. Kurz and P. Patalong, Renormalization of a Lorentz invariant doubled worldsheet theory, JHEP 10 (2014) 114 [arXiv:1308.4418] [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].
C. Klimčík and P. Ševera, Dual non-Abelian duality and the Drinfeld double, Phys. Lett. B 351 (1995) 455 [hep-th/9502122] [INSPIRE].
C. Klimčík and P. Ševera, Poisson-Lie T duality and loop groups of Drinfeld doubles, Phys. Lett. B 372 (1996) 65 [hep-th/9512040] [INSPIRE].
S.P. Chowdhury, Superstring partition functions in the doubled formalism, JHEP 09 (2007) 127 [arXiv:0707.3549] [INSPIRE].
C.D.A. Blair, E. Malek and A.J. Routh, An O(d, d) invariant Hamiltonian action for the superstring, Class. Quant. Grav. 31 (2014) 205011 [arXiv:1308.4829] [INSPIRE].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [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].
P. Patalong, Aspects of non-geometry in string theory, Ph.D. thesis, University of Munich, Munich, Germany (2013).
A. Sevrin and D.C. Thompson, A note on supersymmetric chiral bosons, JHEP 07 (2013) 086 [arXiv:1305.4848] [INSPIRE].
A. Giveon and M. Roček, On non-Abelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, On non-Abelian duality, Nucl. Phys. B 424 (1994) 155 [hep-th/9403155] [INSPIRE].
S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and G. Veneziano, Remarks on non-Abelian duality, Nucl. Phys. B 435 (1995) 147 [hep-th/9409011] [INSPIRE].
S.A. Cherkis and J.H. Schwarz, Wrapping the M-theory five-brane on K3, Phys. Lett. B 403 (1997) 225 [hep-th/9703062] [INSPIRE].
A. Giveon and M. Roček, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [hep-th/9112070] [INSPIRE].
K. Lechner, Selfdual tensors and gravitational anomalies in 4n + 2-dimensions, Nucl. Phys. B 537 (1999) 361 [hep-th/9808025] [INSPIRE].
J. Sonnenschein, Chiral bosons, Nucl. Phys. B 309 (1988) 752 [INSPIRE].
K. Sfetsos, Notes on Poisson-Lie T-duality, private communication (1997).
M. Roček, Linearizing the Volkov-Akulov model, Phys. Rev. Lett. 41 (1978) 451 [INSPIRE].
U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
G. Dall’Agata, E. Dudas and F. Farakos, On the origin of constrained superfields, JHEP 05 (2016) 041 [arXiv:1603.03416] [INSPIRE].
A. Sevrin, Some comments on supersymmetry and the doubled formalism from a worldsheet perspective, talk given at Generalized Geometry and T-dualities , May 13, Simons Center For Geometry and Physics, U.S.A. (2010).
V.G. Drinfeld, Quantum groups, J. Sov. Math. 41 (1988) 898 [Zap. Nauchn. Semin. 155 (1986) 18] [INSPIRE].
D.C. Thompson, Generalised T-duality and integrable deformations, Fortsch. Phys. 64 (2016) 349 [arXiv:1512.04732] [INSPIRE].
C.M. Hull and R.A. Reid-Edwards, Gauge symmetry, T-duality and doubled geometry, JHEP 08 (2008) 043 [arXiv:0711.4818] [INSPIRE].
C.M. Hull and R.A. Reid-Edwards, Non-geometric backgrounds, doubled geometry and generalised T-duality, JHEP 09 (2009) 014 [arXiv:0902.4032] [INSPIRE].
G. Dall’Agata and N. Prezas, Worldsheet theories for non-geometric string backgrounds, JHEP 08 (2008) 088 [arXiv:0806.2003] [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].
I. Bandos, Superstring in doubled superspace, Phys. Lett. B 751 (2015) 408 [arXiv:1507.07779] [INSPIRE].
D. Berman, M 5 on a torus and the three-brane, Nucl. Phys. B 533 (1998) 317 [hep-th/9804115] [INSPIRE].
I. Bandos, On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology, JHEP 08 (2014) 048 [arXiv:1406.5185] [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: 1609.03315
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
Driezen, S., Sevrin, A. & Thompson, D.C. Aspects of the doubled worldsheet. J. High Energ. Phys. 2016, 82 (2016). https://doi.org/10.1007/JHEP12(2016)082
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2016)082