Massless hook field in AdS(d+1) from the holographic perspective

TL;DR

This paper explores the holographic duality for massless mixed-symmetry gauge fields with hook Young diagrams in AdS spaces, deriving boundary correlators and analyzing boundary gauge modes.

Contribution

It provides a systematic solution to the Dirichlet problem for hook fields in AdS and identifies the boundary conformal actions, including higher-derivative structures.

Findings

Explicit solutions for hook field equations in AdS.

Two-point correlation functions for boundary operators.

Identification of boundary conformal hook field actions.

Abstract

We systematically consider the AdS/CFT correspondence for a simplest mixed-symmetry massless gauge field described by hook Young diagram. We introduce the radial gauge fixing and explicitly solve the Dirichlet problem for the hook field equations. Solution finding conveniently splits in two steps. We first define an incomplete solution characterized by a functional freedom and then impose the boundary conditions. The resulting complete solution is fixed unambiguously up to boundary values. Two-point correlation function of hook primary operators is found via the corresponding boundary effective action computed separately in even and odd boundary dimensions. In particular, the higher-derivative action for boundary conformal hook fields is identified with a singular part of the effective action in even dimensions. The bulk/boundary symmetry transmutation within the Dirichlet boundary problem is explicitly studied. It is shown that traces of boundary fields are Stueckelberg-like modes that can be algebraically gauged away so that boundary fields are traceless.