Higher Spins and Matter Interacting in Dimension Three

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 $\lambda =1$.

55 pages + appendices, LaTex. Final version to appear in JHEP

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