Introduction to supergravity 2015: Exercise 7.
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)
Calculate
Dα
Dα
¯D˙α
¯D ˙α ¯Φ|. (3)
You will need to make use of
DCDB − (−1)|B||C|
DBDC V A
= −T D
CB DDV A
+ (−1)|D|(|B|+|C|)
V D
R A
CBD . (4)
References
[1] J. Wess and J. Bagger, “Supersymmetry and supergravity,” Princeton, USA: Univ. Pr. (1992)
259 p
1