A Note on Vectorial AdS$_5$/CFT$_4$ Duality for Spin-$j$ Boundary Theory

TL;DR

This paper extends vectorial AdS$_5$/CFT$_4$ duality to boundary theories with free massless spin-$j$ fields, analyzing their higher-spin bulk duals, calculating one-loop free energies, and exploring cases with infinite higher-spin towers.

Contribution

It introduces a new class of higher-spin theories dual to free massless spin-$j$ boundary fields and computes their one-loop free energies, expanding the scope of holographic dualities.

Findings

One-loop free energy proportional to spin-$j$ doubleton quantity.

Higher-spin theories are defined on rigid AdS$_5$ without gravity.

Infinite tower boundary theories are also considered.

Abstract

The vectorial holographic correspondences between higher-spin theories in AdS$_5$ and free vector models on the boundary are extended to the cases where the latter is described by free massless spin-$j$ field. The dual higher-spin theory in the bulk does not include gravity and can only be defined on rigid AdS$_5$ background with $S^4$ boundary. We discuss various properties of these rather special higher-spin theories and calculate their one-loop free energies. We show that the result is proportional to the same quantity for spin-$j$ doubleton treated as if it is a AdS$_5$ field. Finally, we consider even more special case where the boundary theory itself is given by an infinite tower of massless higher-spin fields.