Shadows, currents, and AdS fields

Conformal totally symmetric arbitrary spin currents and shadow fields in flat space-time of dimension greater than or equal to four are studied. A gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving the Stueckelberg fields. A 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 are studied. The bulk fields are considered in a 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.