Conformal Bootstrap With Slightly Broken Higher Spin Symmetry

TL;DR

This paper develops a method to analyze conformal field theories with nearly unbroken higher spin symmetry, providing new predictions for anomalous dimensions of higher spin currents, including in the 3d Ising model.

Contribution

It introduces a novel approach to solve crossing equations in the double light-cone limit for theories with slightly broken higher spin symmetry, extending known results and making new predictions.

Findings

Reproduces all known anomalous dimensions results.

Predicts anomalous dimensions for higher spin currents in the 3d Ising model.

Provides a framework applicable to arbitrary spacetime dimensions.

Abstract

We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents $\gamma_s$ with large spin $s$. The result depends on the symmetries and the spectrum of the unperturbed conformal field theory. We reproduce all known results and make further predictions. In particular we make a prediction for the anomalous dimensions of higher spin currents in the 3d Ising model.