Abstract
We will use the covariant superform approach to develop a new density formula for mathcal{N} = 2 conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor. We will show that this density formula admits an embedding of the real scalar multiplet of [1]. Upon using the embedding of the tensor multiplet into the real scalar multiplet, we will construct a new higher derivative action of the tensor multiplet in mathcal{N} = 2 conformal supergravity.
Highlights
Solving the ψ3ψ2 BianchiThis arises only from t0Jeψ2ψ and should cancel on its own
We will use the covariant superform approach to develop a new density formula for N = 2 conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor
They are commonly used as compensators in gauge fixing the additional symmetries present in conformal supergravity to get the physical Poincare supergravity
Summary
This arises only from t0Jeψ2ψ and should cancel on its own. As we will show below, it cancels on its own. We did a Fierz rearrangement in coming from the first line to the line. One easy way to see how the last line becomes zero is to understand that ψiψ is anti-symmetric in SU(2) indices i and and proportional to εi. Since Σijk transforms in the 4 irrep of SU(2)-R symmetry, this implies δijΣjmnεkmεin = 0 and the expression in (2.16) goes to zero. One can show that the conjugate Bianchi ψ3ψ2 is automatically satisfied
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