Enhanced Duality in 4D Supergravity

TL;DR

This paper explores the enhanced duality symmetries in 4D supergravity, particularly the Gaillard-Zumino Sp(2n_v, R) duality, and discusses their implications for the structure of divergences and quantum properties of supergravity.

Contribution

It reveals the presence of additional dualities in 4D supergravity beyond U-duality, influencing the understanding of divergences and quantum behavior.

Findings

Enhanced dualities in 4D supergravity determine divergence properties.

Extra dualities may explain unique features of D=4 supergravity amplitudes.

Enhanced symmetries relate to the special status of four dimensions in supergravity.

Abstract

U-duality imposes strong constraints on the structure of divergences in supergravity. But Gaillard-Zumino Sp$(2n_v, \mathbb{R})$ duality in D=4 has more symmetries than U-duality. For example, in $N = 8$ the dimension of Sp(56) is 1596, whereas its U-duality subgroup $E_{7(7)}$ has a dimension of 133. In comparison, in 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 the results of the amplitude loop computations in D-dimensional supergravities and of the special status of D = 4 in this respect.