Higher spin versus renormalization group equations

Abstract

We present a variation of earlier attempts to relate renormalization group equations to higher spin equations. We work with a scalar field theory in 3 dimensions. In this case we show that the classical renormalization group equation is a variant of the Vasiliev higher spin equations with Kleinians on ${\mathrm{AdS}}_{4}$ for a certain subset of couplings. In the large N limit this equivalence extends to the quantum theory away from the conformal fixed points.