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

TL;DR

This paper explores how hyperkahler manifolds can be constructed via a quotient using semichiral superfields, revealing new insights into T-duality and gauged sigma models, with specific examples like Eguchi-Hanson and Taub-NUT.

Contribution

It demonstrates that hyperkahler quotients can be obtained using semichiral superfields, providing a new perspective on hyperkahler manifolds and their T-duals within N=(2,2) supersymmetric models.

Findings

Hyperkahler quotient construction with semichiral superfields preserves hyperkahler structure.

T-duality relates these models to NS5-branes and other T-dual configurations.

Examples include Eguchi-Hanson and Taub-NUT manifolds.

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.