Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.
Anomaly cancellation and one-loop finiteness of 6D half-maximal supergravities
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abstract
We suggest that the surprising one-loop finiteness of 6D half-maximal supergravities recently discovered in \cite{Huang:2025nyr} might be related to anomaly-free $SO(5, 21)$ G-duality symmetry in $(2,0)$ supergravity with 21 tensor multiplets and to anomaly-free $SO(4, 20)$ G-duality symmetry of $(1,1)$ supergravity with 20 vector multiplets. Our argument is reminiscent of the analogous role of the anomaly-free $E_{7(7)}$ G-duality symmetry in the UV finiteness of a maximal 4D supergravity at 3 loops.
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UNVERDICTED 2representative citing papers
Anomaly-free SO(5,21) and SO(4,20) G-duality symmetries are proposed to explain the one-loop finiteness of 6D half-maximal supergravities, by analogy with E_{7(7)} in 4D.
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On anomaly free 4d $\mathcal{N}$=4 and 6d (2,0) conformal supergravities and UV finiteness of Poincar\'e supergravities
Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.
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Anomaly cancellation and one-loop finiteness of 6D half-maximal supergravities
Anomaly-free SO(5,21) and SO(4,20) G-duality symmetries are proposed to explain the one-loop finiteness of 6D half-maximal supergravities, by analogy with E_{7(7)} in 4D.