Abstract
We construct the most general four-dimensional \( \mathcal{N} \) = 4 supergravity coupled to an arbitrary number n of vector multiplets in which the global scaling symmetry is gauged, in addition to a subgroup of SL(2, ℝ) × SO(6, n). The various gaugings are parametrized by an embedding tensor built out of \( 2\left(\begin{array}{c}n+6\\ {}3\end{array}\right)+4\left(n+6\right) \) parameters that satisfy a specific set of quadratic consistency constraints, to which we provide explicit solutions. We also derive the local supersymmetry transformation rules and the equations of motion for the four-dimensional \( \mathcal{N} \) = 4 matter-coupled supergravity with local scaling symmetry. Such supergravity theories do not possess an action, since the scaling symmetry is only an on-shell symmetry of the corresponding ungauged theories.
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Acknowledgments
The author would like to thank Alex Kehagias and Mario Trigiante for comments on the manuscript. The research work was supported by the Hellenic Foundation for Research and Innovation (HFRI) under the 3rd Call for HFRI PhD Fellowships (Fellowship Number: 6554).
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Liatsos, N. \( \mathcal{N} \)=4 Supergravity with Local Scaling Symmetry in Four Dimensions. J. High Energ. Phys. 2024, 101 (2024). https://doi.org/10.1007/JHEP05(2024)101
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DOI: https://doi.org/10.1007/JHEP05(2024)101