Pseudo-hyperkahler Geometry and Generalized Kahler Geometry

Details Pseudo-hyperkahler Geometry and Generalized Kahler Geometry Pseudo-hyperkahler Geometry and Generalized Kahler Geometry

2009-03-13

arxiv.org/abs/0903.2376v4

Lett.Math.Phys.95:211-222,2011

Physics

High Energy Physics

High Energy Physics - Theory

Letters in Mathematical Physics : electronically published version

Scientific paper

10.1007/s11005-010-0456-7

We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show that these solutions correspond to a bi-hermitian metric of signature (2, 2) and a pseudo-hyperkaehler geometry of the target space.

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