Anomalous conformal currents, shadow fields and massive AdS fields

TL;DR

This work develops a fully gauge-invariant description of bosonic, totally symmetric anomalous conformal currents and shadow fields in $d\ge 4$, introducing Stueckelberg and auxiliary fields to formulate differential constraints and conformal transformations with a nontrivial $R^a$. Using a CFT-adapted oscillator formalism and a modified de Donder gauge for corresponding massive AdS fields, the authors establish a precise AdS/CFT dictionary: normalizable bulk modes map to anomalous conformal currents, non-normalizable modes map to anomalous shadow fields, and the bulk on-shell gauge structure matches boundary gauge and global symmetries. They derive gauge-invariant two-point vertices for shadow fields and show their reduction to standard CFT results in Stueckelberg frames, while the light-cone gauge provides a diagonal, tractable formulation relevant for string/gauge dualities. The analysis yields decoupled bulk equations via the modified de Donder gauge, clarifies the role of leftover bulk gauge symmetries in boundary dynamics, and produces explicit expressions for two-point correlators and effective actions, thereby generalizing prior results to arbitrary spin $s$ and setting the stage for fermionic and mixed-symmetry extensions. Overall, the paper offers a systematic, symmetry-based framework for connecting massive AdS fields with boundary anomalous conformal structures, with potential applications to higher-spin/string dualities and light-cone formulations of AdS/CFT.

Abstract

In the framework of gauge invariant approach involving Stueckelberg and auxiliary fields, totally symmetric arbitrary spin anomalous conformal current and shadow field in flat space-time of dimension greater than or equal to four are studied. Gauge invariant differential constraints for such anomalous conformal current and shadow field and realization of global conformal symmetries are obtained. Gauge invariant two-point vertex of the arbitrary spin anomalous shadow field is also obtained. In Stueckelberg gauge frame, the two-point gauge invariant vertex becomes the standard two-point vertex of CFT. Light-cone gauge two-point vertex of the arbitrary spin anomalous shadow field is derived. The AdS/CFT correspondence for arbitrary spin anomalous conformal current and shadow field and the respective normalizable and non-normalizable modes of massive arbitrary spin AdS field is studied. The AdS field is considered in modified de Donder gauge which simplifies considerably the study of AdS/CFT correspondence. We show that on-shell leftover gauge symmetries of bulk massive field are related to gauge symmetries of boundary anomalous conformal current and shadow field, while the modified de Donder gauge condition for bulk massive field is related to differential constraints for boundary anomalous conformal current and shadow field.