N = 2 conformal supergravity from twistor-string theory

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.