Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
Ruben Manvelyan, Karapet Mkrtchyan, Werner Ruehl
TL;DR
The paper analyzes the ultraviolet structure of bulk-to-bulk propagators for higher-spin fields in AdS$_4$ and studies a Higgs-like one-loop interaction that yields a finite bulk mass renormalization. By developing a comprehensive propagator formalism in de Donder and Feynman gauges, the authors reveal a universal ultraviolet behavior and connect the bulk mass shift to boundary anomalous dimensions in the dual CFT$_3$, with a characteristic factor of $(\ell-2)$. They compute the one-loop mass renormalization, showing it is finite and can be absorbed into a finite mass counterterm, consistent with holographic expectations and preserving gauge invariance in the chosen scheme. The results support a concrete AdS/CFT interpretation of mass generation for higher-spin fields and set the stage for including nonlinear higher-spin interactions in future work.
Abstract
The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in $AdS_{4}$ space is analyzed in details. Possible interactions with the Higgs scalar and the corresponding one loop mass renormalization are studied. This mass renormalization is finite and connected with the anomalous dimensions of those currents in the corresponding boundary $CFT_{3}$ that cease to be conserved when the interaction is switched on. In particular it is proportional to $\ell-2$.