Interacting spin-2 fields in three dimensions

TL;DR

This paper explores three-dimensional multi-spin-2 field theories, demonstrating how ghost-free interactions are constrained to tree structures and establishing consistency with dual conformal field theories.

Contribution

It identifies restrictions on interaction terms in 3D multi-spin-2 theories ensuring ghost freedom and couples matter consistently, with explicit analysis for three fields.

Findings

Ghost-free theories are represented by tree graphs.

Secondary constraints remove Boulware-Deser ghosts.

Positive bulk masses are compatible with positive CFT central charge.

Abstract

Using the frame formulation of multi-gravity in three dimensions, we show that demanding the presence of secondary constraints which remove the Boulware-Deser ghosts restricts the possible interaction terms of the theory and identifies invertible frame field combinations whose effective metric may consistently couple to matter. The resulting ghost-free theories can be represented by theory graphs which are trees. In the case of three frame fields, we explicitly show that the requirement of positive masses and energies for the bulk spin-2 modes in AdS$_3$ is consistent with a positive central charge for the putative dual CFT$_2$.