Abstract
N=3 Weyl multiplet in four dimensions was first constructed in J. van Muiden et al. (2017) where the authors used the current multiplet approach to obtain the linearized transformation rules and completed the non-linear variations using the superconformal algebra. The multiplet of currents was obtained by a truncation of the multiplet of currents for the N=4 vector multiplet. While the procedure seems to be correct, the result suffers from several inconsistencies. The inconsistencies are observed in the transformation rules as well as the field dependent structure constants in the corresponding soft algebra. We take a different approach, and compute the transformation rule as well as the corresponding soft algebra by demanding consistency.
Highlights
N extended conformal supergravity in four dimensions is a theory of gravity where the fields form a representation of the su(2, 2|N) superconformal algebra
A multiplet in conformal supergravity which contains all the gauge fields of the superconformal algebra is known as the Weyl multiplet
The Weyl multiplet which consists of a real scalar field of Weyl weight +1 is said to be the dilaton Weyl multiplet, and the other Weyl multiplet is known as the standard Weyl multiplet
Summary
N extended conformal supergravity in four dimensions is a theory of gravity where the fields form a representation of the su(2, 2|N) superconformal algebra. The multiplet of currents for a rigid on-shell multiplet is computed and it is coupled to fields via a first order action to obtain the linearized transformation rules. Non-linear transformation rules are obtained by adding all possible terms to the transformation rule consistent with their Weyl weight, chiral weight, Lorentz and R-symmetry structure and demanding consistency with the superconformal algebra. In this process, to realize this as a theory of gravity where local translations act as general coordinate transformations, one has to impose constrains on some of the.
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