Light-cone gauge cubic interaction vertices for massless fields in AdS(4)

TL;DR

This work addresses the problem of constructing the complete set of light-cone gauge cubic interaction vertices for massless fields of arbitrary spin in $AdS_4$ and realizing the $so(3,2)$ symmetry on the light-cone field space. It develops a systematic method that combines kinematical and dynamical symmetry constraints, introduces a harmonic holomorphic/antiholomorphic sector decomposition, and solves for the cubic vertex to obtain a generating form $p_{[3]}^- = \frac{C_{\rm scalar}^{000}}{z} + V + \bar V$ with holomorphic $V$ and antiholomorphic $\bar V$ built from $V_0$ and $\bar V_0$; helicity-based couplings $C^{\lambda_1\lambda_2\lambda_3}$ and $\bar C^{\lambda_1\lambda_2\lambda_3}$ are restricted by $\lambda_1+\lambda_2+\lambda_3 \ge 1$ and $-\lambda_1-\lambda_2-\lambda_3 \ge 1$. The holomorphic piece reduces to the flat-space vertex under a $z$-dependent factor, indicating a close correspondence with massless cubic vertices in flat space. The results pave the way for higher-order extensions, supersymmetric and mixed-symmetry generalizations, and potential applications to AdS/CFT and higher-spin dynamics.

Abstract

In the framework of light-cone formulation of relativistic dynamics, arbitrary spin massless fields propagating in the four-dimensional AdS space are studied. For such fields, the complete list of light-cone gauge cubic interaction vertices is obtained. Realization of relativistic symmetries on space of light-cone gauge massless AdS fields is also obtained. The light-cone gauge vertices for massless AdS fields take simple form similar to the one for massless fields in the flat space.