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U-duality imposes strong constraints on the structure of divergences in supergravity. But Gaillard-Zumino Sp(2nᵥ, R) duality in 4D, where nᵥ is the number of vectors, has more symmetries than U-duality. For example, in maximal supergravity, dimension of Sp(56) is 1596, whereas its U-duality subgroup E₇₍₇₎, has dimension 133. In comparison, D $> 4$ maximal dualities are U-dualities. We argue that the extra dualities in 4D, enhancing U-duality, determine the properties of perturbative quantum supergravity. The presence/absence of enhanced dualities suggests a possible explanation of known amplitude loop computations in D-dimensional supergravities.
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Рената Каллош (2024) studied this question.
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