Abstract
In the paper [1] we showed that in double space, where all initial coordinates xμ are doubled xμ → y μ , the T-duality transformations can be performed by exchanging places of some coordinates xa and corresponding dual coordinates y a . Here we generalize this result to the case of weakly curved background where in addition to the extended coordinate we will also transform extended argument of background fields with the same operator \( {\widehat{\mathcal{T}}}^a \). So, in the weakly curved background T-duality leads to the physically equivalent theory and complete set of T-duality transformations form the same group as in the flat background. Therefore, the double space represent all T-dual theories in unified manner.
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References
B. Sazdović, T-duality as coordinates permutation in double space, arXiv:1501.01024 [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].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [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].
L. Davidović and B. Sazdović, T-duality in a weakly curved background, Eur. Phys. J. C 74 (2014) 2683 [arXiv:1205.1991] [INSPIRE].
L. Davidović, B. Nikolić and B. Sazdović, T-duality diagram for a weakly curved background, arXiv:1406.5364 [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].
L. Davidović, B. Nikolić and B. Sazdović, Canonical approach to the closed string non-commutativity, Eur. Phys. J. C 74 (2014) 2734 [arXiv:1307.6158] [INSPIRE].
M.J. Duff, Duality Rotations in String Theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].
A. Giveon, E. Rabinovici and G. Veneziano, Duality in String Background Space, Nucl. Phys. B 322 (1989) 167 [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [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].
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.M. Hull, Global aspects of T-duality, gauged σ-models and T-folds, JHEP 10 (2007) 057 [hep-th/0604178] [INSPIRE].
C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].
K. Becker, M. Becker and J. Schwarz, String Theory and M-Theory: A Modern Introduction, Cambridge University Press, (2007).
B. Zwiebach, A First Course in String Theory, Cambridge University Press, (2004).
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [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].
A. Giveon and M. Roček, On nonAbelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].
B. Nikolić and B. Sazdović, D5-brane type-I superstring background fields in terms of type IIB ones by canonical method and T-duality approach, Nucl. Phys. B 836 (2010) 100 [arXiv:1004.1962] [INSPIRE].
A. Giveon, N. Malkin and E. Rabinovici, The Riemann Surface in the Target Space and Vice Versa, Phys. Lett. B 220 (1989) 551 [INSPIRE].
E. Alvarez and M.A.R. Osorio, Duality Is an Exact Symmetry of String Perturbation Theory, Phys. Rev. D 40 (1989) 1150 [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].
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].
I. Bakas and D. Lüst, T-duality, Quotients and Currents for Non-Geometric Closed Strings, arXiv:1505.04004 [INSPIRE].
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ArXiv ePrint: 1503.05580
Work supported in part by the Serbian Ministry of Education and Science, under contract No. 171031.
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Sazdović, B. T-duality as coordinates permutation in double space for weakly curved background. J. High Energ. Phys. 2015, 55 (2015). https://doi.org/10.1007/JHEP08(2015)055
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DOI: https://doi.org/10.1007/JHEP08(2015)055