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

TL;DR

This paper develops gauge invariant two-point vertices for shadow fields in flat space, explores their relation to conformal fields via AdS/CFT, and introduces a simplified higher-derivative Lagrangian framework for arbitrary spin conformal fields.

Contribution

It constructs gauge invariant two-point vertices for shadow fields, connects them to AdS/CFT correspondence using a modified gauge, and proposes a new higher-derivative Lagrangian for conformal fields.

Findings

Gauge invariant two-point vertices match standard CFT vertices in Stueckelberg gauge.

Bulk AdS action evaluated on solutions yields shadow field vertices.

New higher-derivative Lagrangian simplifies conformal field description.

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.