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

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.

41 pages; v2: minor corrections, refs added

References in corpus (5)

• Higher Spins in AdS and Twistorial Holography
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization
• FV-type action for AdS(5) mixed-symmetry fields
• CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Cited by in corpus (13)

• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Conformal correlators of mixed-symmetry tensors
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• Type-B Formal Higher Spin Gravity
• Cubic interactions of arbitrary spin fields in 3d flat space
• Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT
• Geodesic Witten diagrams with anti-symmetric exchange
• Long, partial-short, and special conformal fields
• Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS
• Character Integral Representation of Zeta function in AdS${}_{d+1}$: II. Application to partially-massless higher-spin gravities
• Conformal totally symmetric arbitrary spin fermionic fields
• Conformal Lagrangians from the (formal) near boundary analysis of AdS gauge fields