Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics

TL;DR

This paper develops a systematic method to construct four-dimensional N=2 supersymmetric sigma models on tangent bundles of Hermitian symmetric spaces, deriving explicit Lagrangians and hyperkähler potentials, including for the exceptional space E_6/SO(10)×U(1).

Contribution

It provides a new systematic approach to derive supersymmetric sigma models on tangent and cotangent bundles of Hermitian symmetric spaces, including explicit results for exceptional spaces.

Findings

Derived closed-form Lagrangian on tangent bundles.

Obtained hyperkähler potential on cotangent bundles.

Explicitly worked out the E_6/SO(10)×U(1) case.

Abstract

We address the construction of four-dimensional N=2 supersymmetric nonlinear sigma models on tangent bundles of arbitrary Hermitian symmetric spaces starting from projective superspace. Using a systematic way of solving the (infinite number of) auxiliary field equations along with the requirement of supersymmetry, we are able to derive a closed form for the Lagrangian on the tangent bundle and to dualize it to give the hyperkahler potential on the cotangent bundle. As an application, the case of the exceptional symmetric space E_6/SO(10) \times U(1) is explicitly worked out for the first time.