Abstract
We revisit the construction of N = 2 superconformal multiplets using rheonomic superspace techniques. We apply the result to the derivation of off-shell Poincaré supersymmetric models where a tensor multiplet couples to gravity and to an arbitrary number of vector multiplets. We also analyze gaugings involving the tensor field.
Highlights
With tensor fields and those with their scalar or vector duals are equivalent on-shell, it is not at all clear that they remain equivalent off-shell or when one considers higher order derivative corrections
We apply the result to the derivation of off-shell Poincare supersymmetric models where a tensor multiplet couples to gravity and to an arbitrary number of vector multiplets
This, in turn, affects exact results that could be obtained on the computations of the black hole entropy by means of localization techniques [5,6,7], or on the stability properties of the selected vacuum when including non-perturbative effects
Summary
In this work we will follow a geometric approach to derive the supersymmetry transformations of off-shell N = 2 conformal supergravity and its multiplets, which we will use to construct the action of the various N = 2 multiplets in the so-called Poincare off-shell supergravity. We solve the Bianchi identities on these curvatures by fixing their parameterization requiring that the expansion of the curvatures along the corresponding basis in superspace is given only in terms of the physical fields. This is the so-called rheonomic principle and implies that no additional degrees of freedom have been introduced in the theory. Let us show explicitly this construction by applying it to the fundamental multiplet of conformal supergravity: the Weyl multiplet
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