Abstract
Briefly: using a novel (1, 1) superspace formulation of semichiral sigma models with 4D target space, we investigate if an extended supersymmetry in terms of semichirals is compatible with having a 4D target space with torsion.
In more detail: semichiral sigma models have (2, 2) supersymmetry and Generalized Kähler target space geometry by construction. They can also support (4, 4) supersymmetry and Generalized Hyperkähler geometry, but when the target space is four dimensional indications are that the geometry is restricted to Hyperkähler. To investigate this further, we reduce the model to (1, 1) superspace and construct the extra (on-shell) supersymmetries there. We then find the conditions for a lift to (2, 2) super space and semichiral fields to exist. Those conditions are shown to hold for Hyperkähler geometries. The SU(2) ⊗ U(1) WZW model, which has (4, 4) supersymmetry and a semichiral description, is also investigated. The additional supersymmetries are found in (1, 1) superspace but shown not to be liftable to a (2, 2) semichiral formulation.
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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].
M. Göteman, U. Lindström, M. Roček and I. Ryb, Off-shell N = (4, 4) supersymmetry for new (2, 2) vector multiplets, JHEP 03 (2011) 088 [arXiv:1008.3186] [INSPIRE].
M. Göteman, U. Lindström and M. Roček, Semichiral σ-models with 4D hyperKähler geometry, JHEP 01 (2013) 073 [arXiv:1207.4753] [INSPIRE].
M. Roček, K. Schoutens and A. Sevrin, Off-shell WZW models in extended superspace, Phys. Lett. B 265 (1991) 303 [INSPIRE].
U. Lindström, I. Ryb, M. Roček, R. von Unge and M. Zabzine, T-duality for the S 1 piece in the S 3 × S 1 model, unpublished (2009).
I. Bakas and K. Sfetsos, T duality and world sheet supersymmetry, Phys. Lett. B 349 (1995) 448 [hep-th/9502065] [INSPIRE].
T. Buscher, U. Lindström and M. Roček, New supersymmetric σ models with Wess-Zumino terms, Phys. Lett. B 202 (1988) 94 [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].
M. Gualtieri, Generalized complex geometry, Ph.D. Thesis, Oxford University (2003) [math.DG/0401221] [INSPIRE].
F. Magri and C. Morosi, A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds, Quaderni del Dipartimento di Matematica, Università di Milano (1984).
P.M. Crichigno, The semi-chiral quotient, hyperKähler manifolds and T-duality, JHEP 10 (2012) 046 [arXiv:1112.1952] [INSPIRE].
M. Göteman, N = (4, 4) supersymmetry and T-duality, Symmetry 4 (2012) 603 [arXiv:1208.2166] [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].
J. Bogaerts, A. Sevrin, S. van der Loo and S. Van Gils, Properties of semichiral superfields, Nucl. Phys. B 562 (1999) 277 [hep-th/9905141] [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. Göteman and U. Lindström, Pseudo-hyperKähler geometry and generalized Kähler geometry, Lett. Math. Phys. 95 (2011) 211 [arXiv:0903.2376] [INSPIRE].
U. Lindström, I.T. Ivanov and M. Roček, New N = 4 superfields and σ-models, Phys. Lett. B 328 (1994) 49 [hep-th/9401091] [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].
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ArXiv ePrint: 1411.3906
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Lindström, U. Extended supersymmetry of semichiral sigma models in 4D . J. High Energ. Phys. 2015, 170 (2015). https://doi.org/10.1007/JHEP02(2015)170
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DOI: https://doi.org/10.1007/JHEP02(2015)170