N=2 Conformal Supergravity from Twistor-String Theory

TL;DR

This paper derives N=2 conformal supergravity from twistor-string theory by decomposing N=4 superfields, revealing the physical states within a twistor framework using weighted projective space coordinates.

Contribution

It introduces a method to obtain N=2 conformal supergravity from N=4 twistor superfields through superspace derivatives and representation decomposition.

Findings

Derived N=2 superfield strength from N=4 superfields.

Connected twistor superfields to physical states of N=2 conformal supergravity.

Utilized weighted projective space coordinates in the formulation.

Abstract

A chiral superfield strength in N=2 conformal supergravity at linearized level is obtained by acting two superspace derivatives on N=4 chiral superfield strength which can be described in terms of N=4 twistor superfields. By decomposing SU(4)_R representation of N=4 twistor superfields into the SU(2)_R representation with an invariant U(1)_R charge, the surviving N=2 twistor superfields contain the physical states of N=2 conformal supergravity. These N=2 twistor superfields are functions of homogeneous coordinates of weighted complex projective space WCP^{3|4} where the two weighted fermionic coordinates have weight -1 and 3.