String dualities and modular symmetries in supergravity: a review

Abstract

We review the remarkable interplay between modular symmetries and supergravity, which has led to major advances in both physics and mathematics in recent decades. Our focus will be on four-dimensional models with $\mathcal{N}=1$ and $\mathcal{N}=2$ local supersymmetry. We will look at the early articles on the topic, but also touch on recent developments. These results testify to how supergravity, when supplemented with the appropriate assumptions, can be turned into a unique window into quantum gravity.

21 pages + refs. Invited contribution to "Half a century of Supergravity", eds. A. Ceresole and G. Dall'Agata (Cambridge Univ. Press, to appear)