Gravitational Duality Transformations on (A)dS4

TL;DR

This work develops a first-order, electric-magnetic-type duality for linearized gravity on Minkowski and $(A)dS_4$ backgrounds, showing that a canonical duality rotation leaves bulk second-order dynamics intact while introducing boundary terms in the presence of a cosmological constant. The authors express gravity using $K_\alpha$ and $B_\alpha$ as electric and magnetic fields, perform a $3+1$ split, and implement a shift $\hat{K}^\alpha=K^\alpha-\rho\tilde{e}^\alpha$ with $\rho^2=\sigma_\perp\Lambda$ to absorb $\Lambda$ into the canonical structure, then linearize to obtain a Maxwell-like form in the bulk. The duality maps the linearized constraints to linearized Bianchi identities and, on the boundary, induces a sign-flip of the on-shell action, consistent with holographic double-trace deformations that realize an $SL(2,\mathbb{Z})$ action on boundary correlators; a modified duality that preserves the bulk Hamiltonian is also discussed. These results connect gravitational duality to holography and suggest extensions to higher-spin theories and black-hole backgrounds.

Abstract

We discuss the implementation of electric-magnetic duality transformations in four-dimensional gravity linearized around Minkowski or (A)dS4 backgrounds. In the presence of a cosmological constant duality generically modifies the Hamiltonian, nevertheless the bulk dynamics is unchanged. We pay particular attention to the boundary terms generated by the duality transformations and discuss their implications for holography.