Abstract
We study d = 4, \( \mathcal{N} \) ≥ 5 supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local \( \mathcal{H} \)-symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry.
This result implies, in particular, that if \( \mathcal{N} \) = 5 supergravity at five loop will turn out to be UV divergent, the deformed theory will be BRST inconsistent. If it will be finite, it will be a consequence of nonlinear local supersymmetry and E7-type duality.
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Acknowledgments
We are grateful to our collaborators on earlier related projects: S. Ferrara, D. Freedman, M. Gunaydin, H. Nicolai, T. Ortin, A. Van Proeyen. We had extremely useful discussions of the current work with J. J. Carrasco and R. Roiban. It is our understanding from Z. Bern and J. J. Carrasco that the computation of the UV divergence in \( \mathcal{N} \) = L = 5 might be possible in the future, which stimulated our work.
RK is supported by SITP and by the US National Science Foundation grant PHY- 2014215. YY is supported by Waseda University Grant for Special Research Projects (Project number: 2022C-573).
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Kallosh, R., Yamada, Y. Deformation of d = 4, \( \mathcal{N} \) ≥ 5 supergravities breaks nonlinear local supersymmetry. J. High Energ. Phys. 2023, 156 (2023). https://doi.org/10.1007/JHEP06(2023)156
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DOI: https://doi.org/10.1007/JHEP06(2023)156