Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit

Abstract

We study the slightly broken higher-spin currents in various CFTs with U(1) gauge field, including the tricritical QED, scalar QED, fermionic QED and QED-Gross-Neveu-Yukawa theory. We calculate their anomalous dimension by making use of the classical non-conservation equation and the equations of motion. We find a logarithmic asymptotic behaviour (\gamma_s\sim 16/(N\pi^2)γs∼16/(Nπ2) log s ) of the anomalous dimension at large spin ss, which is different from other interacting CFTs without gauge fields and may indicate certain unique features of gauge theories. We also study slightly broken higher-spin currents of the SU(N)_11 WZW model at d=2+\epsilond=2+ϵ dimensions by formulating them as the QED theory, and we again find its anomalous dimension has a logarithmic asymptotic behaviour with respect to spin. This result resolves the mystery regarding the mechanism of breaking higher spin currents of Virasoro symmetry at d=2+\epsilond=2+ϵ dimensions, and may be applicable to other interesting problems such as the 2+\epsilon2+ϵ expansion of Ising CFT.