Rigid 4D N=2 supersymmetric backgrounds and actions

TL;DR

This paper classifies all four-dimensional N=2 rigid supersymmetric backgrounds with eight supercharges, including various warped geometries, and derives the corresponding vector and hypermultiplet actions with conditions on their target spaces.

Contribution

It provides a comprehensive classification of N=2 supersymmetric backgrounds in 4D and constructs the associated rigid actions, including exotic geometries and conditions on target spaces.

Findings

Identified specific warped geometries preserving supersymmetry.

Derived generic two-derivative actions for vector and hypermultiplets.

Analyzed conditions on special Kahler and hyperkahler target spaces.

Abstract

We classify all N=2 rigid supersymmetric backgrounds in four dimensions with both Lorentzian and Euclidean signature that preserve eight real supercharges, up to discrete identifications. Among the backgrounds we find specific warpings of S^3 x R and AdS_3 x R, AdS_2 x S^2 and H^2 x S^2 with generic radii, and some more exotic geometries. We provide the generic two-derivative rigid vector and hypermultiplet actions and analyze the conditions imposed on the special Kahler and hyperkahler target spaces.