Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model

TL;DR

This paper explores how a singleton deformation in higher-spin theory affects the dual O(N) vector model, leading to a shift in N, symmetry breaking, and anomalous dimensions, thus deepening understanding of holographic dualities.

Contribution

It demonstrates that singleton deformation shifts N to N+1 and derives the boundary gap equations from higher-spin theory, revealing symmetry breaking effects.

Findings

Deformation shifts N to N+1 in the duality.

Singleton couples via a marginal boundary interaction.

Higher-spin symmetry is broken, producing anomalous dimensions.

Abstract

We consider a singleton deformation of the AdS4 higher-spin theory dual to the three-dimensional O(N) vector model. The singleton couples to the higher-spin multiplet only through a marginal boundary interaction. We argue that the effect of such a deformation is to shift N to N+1 in both sides of the holographic correspondance and we show how the gap equations of the three-dimensional O(N) vector model arise from the higher-spin theory. The singleton deformation breaks higher-spin symmetry and gives rise to the well-known 1/N anomalous dimensions of the boundary theory.