Abstract
Non-Abelian T-duality (NATD) is a solution generating transformation for supergravity backgrounds with non-Abelian isometries. We show that NATD can be de-scribed as a coordinate dependent O(d,d) transformation, where the dependence on the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group. Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions. As a result of this embedding, it becomes easy to prove that the NATD transformed backgrounds solve supergravity equations, when the isometry algebra is unimodular. If the isometry algebra is non-unimodular, the generalized dilaton field is forced to have a linear dependence on the dual coordinates, which implies that the resulting background solves generalized supergravity equations.
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References
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].
E. Alvarez, L. Alvarez-Gaume and Y. Lozano, NonAbelian duality in WZW models, (1994) [INSPIRE].
A. Giveon and M. Roček, On nonAbelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [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].
K. Sfetsos and D.C. Thompson, On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys.B 846 (2011) 21 [arXiv:1012.1320] [INSPIRE].
Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond Fields and Coset Geometries, JHEP06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
G. Itsios, Y. Lozano, E. O Colgain and K. Sfetsos, Non-Abelian T-duality and consistent truncations in type-II supergravity, JHEP08 (2012) 132 [arXiv:1205.2274] [INSPIRE].
G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, Non-Abelian T-duality and the AdS/CFT correspondence:new N = 1 backgrounds, Nucl. Phys.B 873 (2013) 1 [arXiv:1301.6755] [INSPIRE].
J. Jeong, O. Kelekci and E. O Colgain, An alternative IIB embedding of F (4) gauged supergravity, JHEP05 (2013) 079 [arXiv:1302.2105] [INSPIRE].
K. Sfetsos and D.C. Thompson, New \( \mathcal{N}=1 \)supersymmetric AdS 5backgrounds in Type IIA supergravity, JHEP11 (2014) 006 [arXiv:1408.6545] [INSPIRE].
E. Caceres, N.T. Macpherson and C. Núñez, New Type IIB Backgrounds and Aspects of Their Field Theory Duals, JHEP08 (2014) 107 [arXiv:1402.3294] [INSPIRE].
N.T. Macpherson, C. Núñez, L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Type IIB supergravity solutions with AdS 5from Abelian and non-Abelian T dualities, JHEP02 (2015) 040 [arXiv:1410.2650] [INSPIRE].
Ö. Kelekci, Y. Lozano, N.T. Macpherson and E. Ó. Colgáin, Supersymmetry and non-Abelian T-duality in type-II supergravity, Class. Quant. Grav.32 (2015) 035014 [arXiv:1409.7406] [INSPIRE].
L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Supergravity solutions with AdS 4from non-Abelian T-dualities, JHEP02 (2016) 061 [arXiv:1511.05991] [INSPIRE].
G. Itsios, Y. Lozano, J. Montero and C. Núñez, The AdS 5non-Abelian T-dual of Klebanov-Witten as a \( \mathcal{N}=1 \)linear quiver from M5-branes, JHEP09 (2017) 038 [arXiv:1705.09661] [INSPIRE].
R. Borsato and L. Wulff, Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings, JHEP08 (2018) 027 [arXiv:1806.04083] [INSPIRE].
G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A.A. Tseytlin, Scale invariance of the η-deformed AdS 5× S 5superstring, T-duality and modified type-II equations, Nucl. Phys.B 903 (2016)262 [arXiv:1511.05795] [INSPIRE].
L. Wulff and A.A. Tseytlin, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP06 (2016) 174 [arXiv:1605.04884] [INSPIRE].
M. Gasperini, R. Ricci and G. Veneziano, A Problem with nonAbelian duality?, Phys. Lett.B 319 (1993) 438 [hep-th/9308112] [INSPIRE].
S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and G. Veneziano, Remarks on nonAbelian duality, Nucl. Phys.B 435 (1995) 147 [hep-th/9409011] [INSPIRE].
M. Hong, Y. Kim and E. Ó. Colgáin, On non-Abelian T-duality for non-semisimple groups, Eur. Phys. J.C 78 (2018) 1025 [arXiv:1801.09567] [INSPIRE].
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept.244 (1994) 77 [hep-th/9401139] [INSPIRE].
M. Fukuma, T. Oota and H. Tanaka, Comments on T dualities of Ramond-Ramond potentials on tori, Prog. Theor. Phys.103 (2000) 425 [hep-th/9907132] [INSPIRE].
Y. Sakatani, Type II DFT solutions from Poisson-Lie T-duality/plurality, arXiv:1903.12175 [INSPIRE].
M. Bugden, Non-abelian T-folds, JHEP03 (2019) 189 [arXiv:1901.03782] [INSPIRE].
A. Catal-Ozer, Non-Abelian T-duality as an O(d, d) transformation, APCTP, Pohang, Korea, (2016) [https://www.apctp.org/plan.php/duality/1341].
A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys.B 350 (1991) 395 [INSPIRE].
A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett.B 242 (1990) 163 [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev.D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev.D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
W. Siegel, Manifest duality in low-energy superstrings, in International Conference on Strings 93, Berkeley, California, 24-29 May 1993, pp. 353-363 (1993) [hep-th/9308133] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
B. Zwiebach, Double Field Theory, T-duality and Courant Brackets, Lect. Notes Phys.851 (2012) 265 [arXiv:1109.1782] [INSPIRE].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP06 (2013) 101 [arXiv:1304.1472] [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].
O. Hohm, S.K. Kwak and B. Zwiebach, Double Field Theory of Type II Strings, JHEP09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
Y. Sakatani, S. Uehara and K. Yoshida, Generalized gravity from modified DFT, JHEP04 (2017) 123 [arXiv:1611.05856] [INSPIRE].
J.-i. Sakamoto, Y. Sakatani and K. Yoshida, Weyl invariance for generalized supergravity backgrounds from the doubled formalism, PTEP2017 (2017) 053B07 [arXiv:1703.09213] [INSPIRE].
D. Lüst and D. Osten, Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality, JHEP05 (2018) 165 [arXiv:1803.03971] [INSPIRE].
S. Demulder, F. Hassler and D.C. Thompson, Doubled aspects of generalised dualities and integrable deformations, JHEP02 (2019) 189 [arXiv:1810.11446] [INSPIRE].
C. Klimčík and P. Ševera, Dual nonAbelian duality and the Drinfeld double, Phys. Lett.B 351 (1995) 455 [hep-th/9502122] [INSPIRE].
C. Klimčík, Poisson-Lie T duality, Nucl. Phys. Proc. Suppl.46 (1996) 116 [hep-th/9509095] [INSPIRE].
F. Hassler, Poisson-Lie T-duality in Double Field Theory, arXiv:1707.08624 [INSPIRE].
R. Blumenhagen, F. Hassler and D. Lüst, Double Field Theory on Group Manifolds, JHEP02 (2015) 001 [arXiv:1410.6374] [INSPIRE].
R. Blumenhagen, P. du Bosque, F. Hassler and D. Lüst, Generalized Metric Formulation of Double Field Theory on Group Manifolds, JHEP08 (2015) 056 [arXiv:1502.02428] [INSPIRE].
F. Hassler, The Topology of Double Field Theory, JHEP04 (2018) 128 [arXiv:1611.07978] [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys.B 153 (1979) 61 [INSPIRE].
J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett.82B (1979) 60 [INSPIRE].
D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP11 (2011) 052 [Erratum ibid.11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
M. Graña and D. Marques, Gauged Double Field Theory, JHEP04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
A. Catal-Ozer, Duality Twisted Reductions of Double Field Theory of Type II Strings, JHEP09 (2017) 044 [arXiv:1705.08181] [INSPIRE].
A. Catal-Ozer, Lunin-Maldacena deformations with three parameters, JHEP02 (2006) 026 [hep-th/0512290] [INSPIRE].
E. Bergshoeff, R. Kallosh, T. Ortín, D. Roest and A. Van Proeyen, New formulations of D = 10 supersymmetry and D8-O8 domain walls, Class. Quant. Grav.18 (2001) 3359 [hep-th/0103233] [INSPIRE].
S. Mukai, Symplectic Structure of the Moduli Space of Sheaves on an Abelian or K3 Surface, Invent. Math.77 (1984) 101.
A. Catal-Ozer, Massive deformations of Type IIA theory within double field theory, JHEP02 (2018) 179 [arXiv:1706.08883] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5× S 5superstring, JHEP04 (2014) 153 [arXiv:1401.4855] [INSPIRE].
B. Hoare and A.A. Tseytlin, Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS 5σ-model, J. Phys.A 49 (2016) 494001 [arXiv:1609.02550] [INSPIRE].
R. Borsato and L. Wulff, Integrable Deformations of T -Dual σ Models, Phys. Rev. Lett.117 (2016) 251602 [arXiv:1609.09834] [INSPIRE].
J.-i. Sakamoto, Y. Sakatani and K. Yoshida, Homogeneous Yang-Baxter deformations as generalized diffeomorphisms, J. Phys.A 50 (2017) 415401 [arXiv:1705.07116] [INSPIRE].
I. Bakhmatov, E. Ó Colgáin, M.M. Sheikh-Jabbari and H. Yavartanoo, Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT), JHEP06 (2018) 161 [arXiv:1803.07498] [INSPIRE].
J.-I. Sakamoto and Y. Sakatani, Local β-deformations and Yang-Baxter σ-model, JHEP06 (2018)147 [arXiv:1803.05903] [INSPIRE].
I. Bakhmatov and E.T. Musaev, Classical Yang-Baxter equation from β-supergravity, JHEP01 (2019) 140 [arXiv:1811.09056] [INSPIRE].
T. Araujo, I. Bakhmatov, E. Ó. Colgáin, J. Sakamoto, M.M. Sheikh-Jabbari and K. Yoshida, Yang-Baxter σ-models, conformal twists and noncommutative Yang-Mills theory, Phys. Rev. D95 (2017) 105006 [arXiv:1702.02861] [INSPIRE].
T. Araujo, I. Bakhmatov, E. Ó. Colgáin, J.-i. Sakamoto, M.M. Sheikh-Jabbari and K. Yoshida, Conformal twists, Yang-Baxter σ-models & holographic noncommutativity, J. Phys. A51 (2018) 235401 [arXiv:1705.02063] [INSPIRE].
A. Çatal Özer and S. Tunalı, Yang-Baxter Deformation as an O(d, d) Transformation, arXiv:1906.09053 [INSPIRE].
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Çatal-Özer, A. Non-Abelian T-duality as a transformation in Double Field Theory. J. High Energ. Phys. 2019, 115 (2019). https://doi.org/10.1007/JHEP08(2019)115
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DOI: https://doi.org/10.1007/JHEP08(2019)115