Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT

TL;DR

This paper explores mixed-symmetry fields in AdS(5), their conformal counterparts in 4d, and their roles in the AdS/CFT correspondence, including gauge actions, boundary currents, shadows, and divergence behaviors.

Contribution

It develops light-cone gauge formulations for mixed-symmetry fields and establishes their AdS/CFT correspondence, linking bulk modes to boundary conformal fields and analyzing UV divergences.

Findings

Light-cone gauge actions lead to decoupled equations of motion.

Bulk modes correspond to boundary conformal currents and shadows.

UV divergences relate to long and short conformal fields.

Abstract

Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field evaluated on solution of the Dirichlet problem amounts to the light-cone gauge 2-point vertex of mixed-symmetry anomalous shadow. Also we show that UV divergence of the action for mixed-symmetry massive AdS field with some particular value of mass parameter evaluated on the Dirichlet problem amounts to the action of long mixed-symmetry conformal field, while UV divergence of the action for mixed-symmetry massless AdS field evaluated on the Dirichlet problem amounts to the action of short mixed-symmetry conformal field. We speculate on string theory interpretation of a model which involves short low-spin conformal fields and long higher-spin conformal fields.