Partially Massless Higher-Spin Theory

TL;DR

This paper extends Vasiliev's higher-spin theory to include partially massless fields, resulting in a non-linear, UV-complete theory that matches dual CFT predictions and exhibits unique features in specific dimensions.

Contribution

It introduces a generalized higher-spin algebra with third-order Killing tensors and constructs a fully non-linear, UV-complete theory including gravity and partially massless fields.

Findings

Masses of non-fixed particles match CFT predictions

The theory truncates in D=3,5 dimensions

Non-diagonalizable mixings occur in D=4,7

Abstract

We study a generalization of the D-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that includes "third-order" Killing tensors. Gauging this algebra with the Vasiliev formalism leads to a fully non-linear theory which is expected to be UV complete, includes gravity, and can live on dS as well as AdS. The linearized spectrum includes three massive particles and an infinite tower of partially massless particles, in addition to the usual spectrum of particles present in the Vasiliev theory, in agreement with predictions from a putative dual CFT with the same symmetry algebra. We compute the masses of the particles which are not fixed by the massless or partially massless gauge symmetry, finding precise agreement with the CFT predictions. This involves computing several dozen of the lowest-lying terms in the expansion of the trilinear form of the enlarged higher-spin algebra. We also discuss nuances in the theory that occur in specific dimensions; in particular, the theory dramatically truncates in bulk dimensions D=3,5 and has non-diagonalizable mixings which occur in D=4,7.