Introduction to supergravity 2015: Exercise 4.
Institute for Theoretical Physics, Masaryk University,
611 37 Brno, Czech Republic
Here we work with the linearized old-minimal supergravity [1]. Prove the following Bianchi
identities for the supergravity superfields Gα ˙α and R
(Ga)∗
= Ga, (1)
and
¯D ˙α
Gα ˙α = DαR. (2)
Calculate the highest component of the chiral superfield R
−
1
4
D2
R| (3)
in the appropriate WZ gauge. Which gravitational object resides in this component?
References
[1] S. Ferrara and B. Zumino, “Structure of Conformal Supergravity,” Nucl. Phys. B 134, 301
(1978).
1