Gauge invariant two-point vertices of shadow fields, AdS/CFT, and conformal fields

TL;DR

The paper develops a gauge-invariant Stueckelberg framework for totally symmetric shadow fields of arbitrary spin in $d\ge4$, deriving two-point vertices and connecting them to standard CFT and light-cone formulations. It then applies a modified Lorentz/de Donder gauge in AdS$_{d+1}$ to study the AdS/CFT correspondence, showing that bulk actions on Dirichlet solutions reproduce the boundary shadow vertices and yield a new, simple higher-derivative description of conformal fields with Stueckelberg gauge symmetries. Explicit results are provided for scalar, spin-1, spin-2, and arbitrary spin, including the corresponding conformal-field Lagrangians and their light-cone forms, together with the normalization factors that relate AdS effective actions to the standard two-point vertices. The framework offers a unifying approach to conformal currents/shadow fields and higher-spin holography, with clear paths to extensions to anomalous currents, fermions, higher-point vertices, mixed-symmetry fields, and infinite higher-spin towers in AdS/CFT.

Abstract

In the framework of gauge invariant Stueckelberg approach, totally symmetric arbitrary spin shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant two-point vertices for such shadow fields are obtained. We demonstrate that, in Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of CFT. Light-cone gauge two-point vertices of the shadow fields are also obtained. AdS/CFT correspondence for the shadow fields and the non-normalizable solutions of free massless totally symmetric arbitrary spin AdS fields is studied. AdS fields are considered in a modified de Donder gauge and this simplifies considerably the study of AdS/CFT correspondence. We demonstrate that the bulk action, when it is evaluated on solution of the Dirichlet problem, leads to the two-point gauge invariant vertex of shadow field. Also we shown that the bulk action evaluated on solution of the Dirichlet problem leads to new description of conformal fields. The new description involves Stueckelberg gauge symmetries and gives simple higher-derivative Lagrangian for the conformal arbitrary spin field. In the Stueckelberg gauge frame, our Lagrangian becomes the standard Lagrangian of conformal field. Light-cone gauge Lagrangian of the arbitrary spin conformal field is also obtained.