The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality

Abstract

We study the construction of generalized Kahler manifolds, described purely in terms of N=(2,2) semichiral superfields, by a quotient using the semichiral vector multiplet. Despite the presence of a b-field in these models, we show that the quotient of a hyperkahler manifold is hyperkahler, as in the usual hyperkahler quotient. Thus, quotient manifolds with torsion cannot be constructed by this method. Nonetheless, this method does give a new description of hyperkahler manifolds in terms of two-dimensional N=(2,2) gauged non-linear sigma models involving semichiral superfields and the semichiral vector multiplet. We give two examples: Eguchi-Hanson and Taub-NUT. By T-duality, this gives new gauged linear sigma models describing the T-dual of Eguchi-Hanson and NS5-branes. We also clarify some aspects of T-duality relating these models to N=(4,4) models for chiral/twisted-chiral fields and comment briefly on more general quotients that can give rise to torsion and give an example.

31 pages

References in corpus (8)

• Double Field Theory
• The KK-Monopole/NS5-Brane in Doubled Geometry
• T-duality and Generalized Kahler Geometry
• New N = (2, 2) vector multiplets
• The generalized Kaehler geometry of N=(2,2) WZW-models
• T-duality, quotients and generalized Kahler geometry
• Nonabelian Generalized Gauge Multiplets
• The general (2,2) gauged sigma model with three--form flux

Cited by in corpus (6)

• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Extended supersymmetry of semichiral sigma model in 4D
• Dynamics of Two-Dimensional $\mathcal{N}=(2,2)$ Supersymmetric Theories with Semichiral Superfields I
• Semichiral Sigma Models with 4D Hyperkaehler Geometry
• T-Duality in $(2,1)$ Superspace