Electric-Magnetic Duality in Supergravity

TL;DR

The paper presents a comprehensive review of electric-magnetic duality in four-dimensional extended supergravity, casting dualities as symplectic reparametrizations in $Sp(2n,R)$ and showing how they act on the vector sector and scalar manifolds. It highlights the emergence of hidden symmetries, notably $E_{7(7)}$ for $N=8$ supergravity, and explains how these symmetries organize the couplings via coset spaces $G/H$ and generalized vielbeins, even as gauging can break the full duality. The discussion of matter couplings in $N=2$ theories emphasizes the role of the holomorphic prepotential $F(X)$ and the distinction between duality invariance and equivalence classes of theories connected by symplectic transformations. In the presence of chiral backgrounds and higher-derivative couplings, duality preserves certain symplectic functions (e.g., $F_A$) while generating a hierarchy of transformed derivatives, shedding light on holomorphic anomalies and their relation to topological string amplitudes and black-hole entropy. Overall, the work clarifies how duality constrains and structures the low-energy effective actions of supergravity and string/M-theory, with implications for entropy, BPS spectra, and nonperturbative dynamics.

Abstract

I review electric-magnetic duality from the perspective of extended supergravity theories in four spacetime dimensions