Introduction to supergravity 2015: Exercise 9.
Institute for Theoretical Physics, Masaryk University,
611 37 Brno, Czech Republic
Our conventions can be found in [1], and we work with the Lagrangian
L = d4
θ ¯ΦeV
Φ +
1
4g2
d2
θ Wα
(V )Wα(V ) + c.c. + 2ξ d4
θ V (1)
where
Wα(V ) = −
1
4
¯D2
DαV (2)
and g is the dimensionless gauge coupling and ξ is a constant of dimension [ξ] = 2. When we turn
to WZ gauge, the exponential becomes
eV
|WZ = 1 + V +
1
2
V 2
. (3)
1. Write the component form of (1) in the WZ gauge. Write both the fermionic and the bosonic sector.
2. Integrate out the auxiliary fields, and write down the full model.
3. What happens for ξ > 0? What happens for ξ = 0? What happens for ξ < 0?
References
[1] J. Wess and J. Bagger, “Supersymmetry and supergravity,” Princeton, USA: Univ. Pr. (1992).
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