Introduction to supergravity 2015: Exercise 6.
Institute for Theoretical Physics, Masaryk University,
611 37 Brno, Czech Republic
Our superspace conventions are found in [1]. The components of the chiral superfield
¯D˙αΦ = 0 (1)
are defined as
Φ| = A
1
√
2
DαΦ| = χα
−
1
4
D2
Φ| = F.
(2)
We saw that the local supersymmetry transformations (or supergauge transformations) for the
chiral superfield are given by
δΦ = −ξA
DAΦ. (3)
Note that if the superfield Φ was not a Lorentz scalar this supergauge transformation would be
accompanied by the appropriate compensating field dependent change of frame such that we stay
in the WZ gauge for the gravitational multiplet.
By using the components definition (2) and the transformation definition (3) find the transformation
for the component fields of the chiral superfield
δA =?
δχα =?
δF =?
(4)
and express your results in terms of supercovariant derivatives.
References
[1] J. Wess and J. Bagger, “Supersymmetry and supergravity,” Princeton, USA: Univ. Pr. (1992)
259 p
1