Abstract
We study generalized Kähler structures on N = (2, 2) supersymmetric WessZumino-Witten models; we use the well known case of SU(2) × U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the highly nontrivial structure of the hitherto unexplored case of SU(3); these tools should be useful for studying many other examples. We find that different generalized Kähler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models can be found by T-duality transformations along affine isometries.
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References
B. Zumino, Supersymmetry and Kähler manifolds, Phys. Lett. B 87 (1979) 203 [INSPIRE].
S.J. Gates, Jr., C.M. Hull and M. Roček, Twisted multiplets and new supersymmetric nonlinear σ-models, Nucl. Phys. B 248 (1984) 157 [INSPIRE].
T. Buscher, U. Lindström and M. Roček, New supersymmetric σ models with Wess-Zumino terms, Phys. Lett. B 202 (1988) 94 [INSPIRE].
A. Sevrin and J. Troost, Off-shell formulation of N = 2 nonlinear σ-models, Nucl. Phys. B 492 (1997) 623 [hep-th/9610102] [INSPIRE].
M.T. Grisaru, M. Massar, A. Sevrin and J. Troost, Some aspects of N = (2, 2), D = 2 supersymmetry, Fortsch. Phys. 47 (1999) 301 [hep-th/9801080] [INSPIRE].
U. Lindström, M. Roček, R. von Unge and M. Zabzine, Generalized Kähler manifolds and off-shell supersymmetry, Commun. Math. Phys. 269 (2007) 833 [hep-th/0512164] [INSPIRE].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. 54 (2003) 281 [math.DG/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Oxford U., Oxford U.K., (2003) [math.DG/0401221] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Supersymmetric backgrounds from generalized Calabi-Yau manifolds, JHEP 08 (2004) 046 [hep-th/0406137] [INSPIRE].
C. Jeschek and F. Witt, Generalised G 2 -structures and type IIB superstrings, JHEP 03 (2005) 053 [hep-th/0412280] [INSPIRE].
T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
I.T. Ivanov, B.-B. Kim and M. Roček, Complex structures, duality and WZW models in extended superspace, Phys. Lett. B 343 (1995) 133 [hep-th/9406063] [INSPIRE].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
P. Spindel, A. Sevrin, W. Troost and A. Van Proeyen, Extended supersymmetric σ-models on group manifolds. 1. The complex structures, Nucl. Phys. B 308 (1988) 662 [INSPIRE].
M. Roček, K. Schoutens and A. Sevrin, Off-shell WZW models in extended superspace, Phys. Lett. B 265 (1991) 303 [INSPIRE].
K. Yano, Differential geometry on complex and almost complex spaces, Pergamon Press, Oxford U.K., (1965).
C.M. Hull, A. Karlhede, U. Lindström and M. Roček, Nonlinear σ models and their gauging in and out of superspace, Nucl. Phys. B 266 (1986) 1 [INSPIRE].
A. Sevrin, W. Staessens and D. Terryn, The generalized Kähler geometry of N = (2, 2) WZW-models, JHEP 12 (2011) 079 [arXiv:1111.0551] [INSPIRE].
U. Lindström, Extended supersymmetry of semichiral σ-models in 4D, JHEP 02 (2015) 170 [arXiv:1411.3906] [INSPIRE].
C.M. Hull, U. Lindström, M. Roček, R. von Unge and M. Zabzine, Generalized Kähler geometry and gerbes, JHEP 10 (2009) 062 [arXiv:0811.3615] [INSPIRE].
M.T. Grisaru, M. Massar, A. Sevrin and J. Troost, The quantum geometry of N = (2, 2) nonlinear σ-models, Phys. Lett. B 412 (1997) 53 [hep-th/9706218] [INSPIRE].
C.M. Hull, U. Lindström, M. Roček, R. von Unge and M. Zabzine, Generalized Calabi-Yau metric and generalized Monge-Ampere equation, JHEP 08 (2010) 060 [arXiv:1005.5658] [INSPIRE].
U. Lindström, M. Roček, I. Ryb, R. von Unge and M. Zabzine, New N = (2, 2) vector multiplets, JHEP 08 (2007) 008 [arXiv:0705.3201] [INSPIRE].
U. Lindström, M. Roček, I. Ryb, R. von Unge and M. Zabzine, T-duality and generalized Kähler geometry, JHEP 02 (2008) 056 [arXiv:0707.1696] [INSPIRE].
U. Lindström, M. Roček, I. Ryb, R. von Unge and M. Zabzine, Non-Abelian generalized gauge multiplets, JHEP 02 (2009) 020 [arXiv:0808.1535] [INSPIRE].
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Ang, J.P., Driezen, S., Roček, M. et al. Generalized Kähler structures on group manifolds and T-duality. J. High Energ. Phys. 2018, 189 (2018). https://doi.org/10.1007/JHEP05(2018)189
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DOI: https://doi.org/10.1007/JHEP05(2018)189