Chern-Simons vector models and higher spins - Ginzburg ...

Higher spin symmetry at large NWhat happens is that, at finite N, J s can (and does) combine with“multi-trace” operators. The non-conservation equation takes theschematic form∂ · J s ∼ f √ (λ) ∑∂ m J s1 ∂ n J s2 + g(λ) ∑∂ m J s1 ∂ n J s2 ∂ p J s3N NThe argument above implies that the HS currents do not haveanomalous dimensions in the planar limit. But one can in fact arguethat the scalar J 0 has protected dimension as well∆(J 0 ) = 2 + O( 1 N )which we have checked perturbatively to two-loop order.Simone Giombi (PI) Chern-Simons and higher spins Lebedev Inst., Jun 1 2012 20 / 24