N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

Chapter 3
The Linear Case
In this chapter we present the linear vector-tensor multiplet with gauged central charge.
Starting from the consistency conditions derived in the previous chapter, we determine
the constraints that underlie the model and work out the supersymmetry and central
charge transformations of the component fields. The Bianchi identities will be computed
and solved in terms of gauge potentials. Then we follow the procedure outlined
in sections 1.2 and 2.3.1 in order to derive an invariant action. After generalizing
the model to include couplings to additional nonabelian vector multiplets, we conclude
with a brief review of Henneaux-Knaepen models and their relation to the vector-tensor
multiplet.
3.1 Consistent Constraints
Having singled out two possible coefficient functions F in the previous chapter, we shall
now attempt to solve the consistency conditions (2.79) subject to the first solution
F1 = 0.
Eqs. 4) and 5) are satisfied identically, while from eqs. 1) and 19) we infer that A does
not depend on L. The same holds for E according to eq. 6). Now consider eq. 10),
The general solution is given by A1 = 0 and
A2 =
∂A = 1
2 A2 . (3.1)
2
¯h( ¯ Z) − Z
, (3.2)
where ¯ h is an arbitrary function of ¯ Z. Next let us differentiate eq. 25) with respect to
L; using eq. 2) it follows that
0 = 1 + 1 1 ZA + 2 2 ¯ ZĀ + ZCF + ¯ Z ¯ C ¯ F . (3.3)
With F = 0 we find
A + 2
Z = − ¯ Z
Ā ,
Z
(3.4)
which excludes first of all the solution A1 = 0. When inserted into eq. 9) we obtain
¯∂A = 1AĀ
, (3.5)
2
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