Shadows, currents and AdS fields

TL;DR

The paper develops a gauge-invariant framework for conformal currents and shadow fields of arbitrary spin in $d\ge4$ by introducing Stueckelberg-type fields and nontrivial $R^a$ realizations that preserve global conformal symmetries. It constructs explicit gauge-invariant formulations for spin-1, spin-2, and arbitrary spin currents and shadows, together with their two-point interaction vertices, all organized to be compatible with AdS/CFT, using modified Lorentz and de Donder gauges to obtain decoupled bulk equations. The work demonstrates how leftover bulk gauge symmetries map to boundary current/shadow gauge symmetries, and establishes precise bulk-boundary correspondences for normalizable and non-normalizable AdS modes with the corresponding boundary data. It further clarifies the interrelations between gauge-invariant conformal field theories and massive field theories in flat space, via controlled breaking of conformal symmetry ($\Box \to m^2$), yielding a unified Stueckelberg-like perspective across the AdS/CFT and flat-space regimes.

Abstract

Conformal totally symmetric arbitrary spin currents and shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal boost symmetries is obtained. Gauge invariant differential constraints for currents and shadow fields are obtained. AdS/CFT correspondence for currents and shadow fields and the respective normalizable and non-normalizable solutions of massless totally symmetric arbitrary spin AdS fields is studied. The bulk fields are considered in modified de Donder gauge that leads to decoupled equations of motion. We demonstrate that leftover on-shell gauge symmetries of bulk fields correspond to gauge symmetries of boundary currents and shadow fields, while the modified de Donder gauge conditions for bulk fields correspond to differential constraints for boundary conformal currents and shadow fields. Breaking conformal symmetries, we find interrelations between the gauge invariant formulation of the currents and shadow fields and the gauge invariant formulation of massive fields.