The masses of gauge fields in higher spin field theory on AdS(4)

TL;DR

This work analyzes higher spin gauge fields on AdS$_4$ arising from lifting the 3D O(N) vector sigma model (HS(4)) and demonstrates that their masses can be computed perturbatively from anomalous dimensions in the underlying flat CFT. By performing a conformal partial wave decomposition of bilocal correlators and carefully accounting for radiative corrections, the authors extract the leading anomalous dimensions $\eta_1(l)$, obtaining $\eta_1(2)=0$ and, for $d=3$, $\eta_1(l)=\frac{16(l-2)}{3\pi^2(2l-1)}$ for $l\ge4$. Consequently, the AdS masses satisfy $m(l)^2=\frac{16}{3N\pi^2}(l-2)+O(1/N^2)$, showing a Regge-like linear dependence on spin and supporting a Higgs-like mechanism for gauge fields (except the graviton due to boundary conditions). The results hint at an underlying string-theoretic description of HS(4) in AdS$_4$.

Abstract

Higher spin field theory on AdS(4) is defined by lifting the minimal conformal sigma model in three dimensional flat space. This allows to calculate the masses from the anomalous dimensions of the currents in the sigma model. The Goldstone boson field can be identified

Figures (4)

• Figure 1: The disconnected graphs $A_1$ and $A_3$
• Figure 2: The graph $B_{2}$ and its complete radiatively corrected form $B_{2}^{com}$
• Figure 3: The crossed exchange graphs.
• Figure 4: The box graphs.