Cotangent bundle over Hermitian symmetric space $E_7/E_6 \times U(1)$ from projective superspace

TL;DR

This paper constructs an $ ext{N}=2$ supersymmetric sigma model on the cotangent bundle of a specific Hermitian symmetric space using projective superspace, providing a new general formula applicable to all such spaces.

Contribution

It develops a new closed formula for cotangent bundle actions on Hermitian symmetric spaces within the projective superspace formalism.

Findings

Derived a universal formula for cotangent bundle actions

Connected cotangent bundle structure to Kähler potential rescaling

Extended supersymmetric sigma models to complex symmetric spaces

Abstract

We construct an $\mathcal{N}$ supersymmetric sigma model on the cotangent bundle over the Hermitian symmetric space $E_7/(E_6\times U(1))$ in the projective superspace formalism, which is a manifest $\mathcal{N}=2$ off-shell superfield formulation in four-dimensional spacetime. To obtain this model we elaborate on results developed in arXiv:0811.0218 and present a new closed formula for the cotangent bundle action, which is valid for all Hermitian symmetric spaces. We show that the structure of cotangent bundle action is intimately related to the analytic structure of the K\"ahler potential with respect to a uniform rescaling of coordinates.