Higher Spins and Matter Interacting in Dimension Three

TL;DR

This paper analyzes a specific higher-spin theory in three dimensions, identifying a unique consistent truncation that avoids extra sectors, and explicitly computes the backreaction and cubic interactions of the physical fields.

Contribution

It finds a unique truncation of Prokushkin--Vasiliev Theory in AdS3 that eliminates problematic sectors and fully determines the cubic action for physical fields.

Findings

Explicit second-order backreaction computed

Unique truncation avoiding extra sectors identified

Cubic action for physical fields fully determined

Abstract

The spectrum of Prokushkin--Vasiliev Theory is puzzling in light of the Gaberdiel--Gopakumar conjecture because it generically contains an additional sector besides higher-spin gauge and scalar fields. We find the unique truncation of the theory avoiding this problem to order 2 in perturbations around AdS$_3$. The second-order backreaction on the physical gauge sector induced by the scalars is computed explicitly. The cubic action for the physical fields is determined completely. We comment on a different higher-spin theory without such additional fields at $\lambda=1$.