Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization

TL;DR

This paper analyzes the ultraviolet singularities of higher spin gauge field propagators in AdS4, examines their interactions with a Higgs scalar, and finds that one-loop mass renormalization is finite and related to boundary CFT anomalous dimensions.

Contribution

It provides a detailed analysis of the UV behavior of higher spin propagators in AdS4 and connects mass renormalization to boundary CFT anomalous dimensions.

Findings

Mass renormalization is finite.

Renormalization is proportional to bcl-2.

Boundary currents acquire anomalous dimensions.

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 $\ell-2$.