N = 3 Conformal Supergravity in Four Dimensions

Abstract

In this paper, we derive the action for $N=3$ conformal supergravity in four space-time dimensions. We construct a density formula for $N=3$ conformal supergravity based on the super form action principle. Finally, we embed the $N=3$ Weyl multiplet in the density formula to obtain the invariant action for $N=3$ conformal supergravity. There are two inequivalent embeddings by changing a particular coefficient from real to imaginary. They lead to invariant actions, which will either be the supersymmetrization of the Weyl square term or the Pontryagin density in the eventuality of gauge fixing to Poincaré supergravity. As a consistency check of our formalism, we will show that the supersymmetrization of the Pontryagin density is a total derivative. We will demonstrate this for purely bosonic terms. We will also present the complete action for the supersymmetrization of the Weyl square term. We also discuss consistent truncation of $N=4$ Weyl multiplet to $N=3$ Weyl multiplet and use it for a robust check of our results using the earlier known results in $N=4$ conformal supergravity.

34 pages,minor fixes

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Cited by in corpus (9)

• Higher Derivative Supergravities in Diverse Dimensions
• Extended superconformal higher-spin gauge theories in four dimensions
• Higher derivative invariants in four dimensional N=3 Poincare supergravity
• N=2 conformal supergravity in five dimensions
• Dilaton Weyl multiplets for $N=3$ conformal supergravity in four dimensions
• Scalar-Tensor multiplet in four dimensional N=2 conformal supergravity
• Geometric distances between closed universes
• Variant dilaton Weyl Multiplet for N=3 conformal supergravity in four dimensions
• Only Flat Spacetime is Full BPS in Four Dimensional N=3 and N=4 Supergravity