Abstract
We present the full Lagrangian and supersymmetry transformation rules for the gauged D = 4, \( \mathcal{N} \) = 4 (half-maximal) supergravity coupled to an arbitrary number of vector multiplets. Using the embedding tensor formulation, the final results are universal and valid in arbitrary symplectic frames. We also analyze the conditions for the critical points of the scalar potential and specify the full spectrum of the quadratic fluctuations about Minkowski vacua. This allows us also to exclude the appearance of quadratic divergences in the 1-loop corrections to the scalar potential for any Minkowski vacuum fully breaking supersymmetry. We also provide some interesting byproducts of our analysis, like the field equations and the quadratic constraints for the fermion shifts characterizing the gauging (also known as T-tensor identities).
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Acknowledgments
G.D. would like to thank S. De Angelis and D. Partipilo for discussions and preliminary calculations that led to revisit gauged \( \mathcal{N} \) = 4 supergravity. This work is supported in part by MIUR-PRIN contract 2017CC72MK00, the MUR Excellent Departments Project 2023-2027. The research work was also supported by the Hellenic Foundation for Research and Innovation (HFRI) under the 3rd Call for HFRI PhD Fellowships (Fellowship Number: 6554). N.L. would like to thank the University of Padova for hospitality during the early stages of the project. R.N. acknowledges GACR grant EXPRO 20-25775X for financial support.
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Dall’Agata, G., Liatsos, N., Noris, R. et al. Gauged D = 4 \( \mathcal{N} \) = 4 supergravity. J. High Energ. Phys. 2023, 71 (2023). https://doi.org/10.1007/JHEP09(2023)071
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DOI: https://doi.org/10.1007/JHEP09(2023)071