Holographic Aspects of Electric-Magnetic Dualities

TL;DR

This work surveys how generalized electric-magnetic dualities manifest holographically in AdS_4/CFT_3 for theories with conformally coupled scalars and abelian gauge fields, clarifying how bulk dualities translate into boundary transformations and deformations. It presents a suite of concrete results: a toy scalar model with a nonlocal alpha–beta boundary relation and a dimension-1 boundary operator, an M-theory embedding with self-dual boundary conditions and exact DBT potentials, a detailed picture of S-duality and boundary Chern-Simons terms for gauge fields, and a gravity extension showing a gravity-specific self-duality constraint on boundary data. Together, these findings illuminate duality-invariant structures in M-theory holography, reveal how three-dimensional boundary theories encode bulk dualities, and expose potential instabilities of AdS_4 vacua via instanton processes. The results also point toward a deeper role for parity anomalies and boundary terms in organizing the holographic dictionary for higher-spin gravity and M-theory compactifications.

Abstract

We review recent work on holographic aspects of electric-magnetic dualities in theories that involve conformally coupled scalars and abelian gauge fields in asymptotically AdS4 spaces. Such models are relevant for the holographic description of M-theory. We also briefly comment on some new results on the holographic properties of generalized electric-magnetic duality in gravity.