Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces

TL;DR

This paper develops a chiral superfield-based on-shell formulation for hyperkaehler sigma-models on cotangent bundles of Hermitian symmetric spaces, providing universal formulas for the hyperkaehler potential and Kähler potential.

Contribution

It introduces a new universal representation for the hyperkaehler potential and a closed-form Kähler potential for Hermitian symmetric spaces within supersymmetric sigma-models.

Findings

Derived a universal hyperkaehler potential in terms of base space curvature.

Provided a new universal formula for the superspace Lagrangian.

Obtained a closed-form Kähler potential in normal coordinates.

Abstract

Starting with the projective-superspace off-shell formulation for four-dimensional N = 2 supersymmetric sigma-models on cotangent bundles of arbitrary Hermitian symmetric spaces, their on-shell description in terms of N = 1 chiral superfields is developed. In particular, we derive a universal representation for the hyperkaehler potential in terms of the curvature of the symmetric base space. Within the tangent-bundle formulation for such sigma-models, completed recently in arXiv:0709.2633 and realized in terms of N = 1 chiral and complex linear superfields, we give a new universal formula for the superspace Lagrangian. A closed form expression is also derived for the Kaehler potential of an arbitrary Hermitian symmetric space in Kaehler normal coordinates.