N=2 Conformal Superspace in Four Dimensions

TL;DR

This paper develops a new geometric formulation of four-dimensional N=2 superspace where the full conformal algebra is realized linearly, extending previous N=1 results and connecting to existing supergravity frameworks.

Contribution

It introduces a novel N=2 conformal superspace geometry with a linear realization of the entire conformal algebra, unifying and extending prior formalisms.

Findings

Explicit realization of SU(2,2|2) in N=2 superspace

Lifts N=2 superconformal tensor calculus to superspace

Reproduces known N=2 conformal supergravity when degauged

Abstract

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.