Large Spin Perturbation Theory

TL;DR

This work introduces twist conformal blocks as a tool to analyze CFTs near points of large twist degeneracy. By decomposing degenerate correlators into $H^{(0)}_ au$ and their deformations $H^{(\\rho)}_ au$, the authors recast crossing into an algebraic problem and derive perturbative spectra around generalised free fields, including all-orders-in-spin results in key cases. In 2D, the twist-block expansion factorizes and yields explicit anomalous-dimension formulas, illuminating the structure of large-spin perturbations. The approach connects twist conformal blocks to higher-spin conformal blocks, clarifying their relationship and suggesting broad applications to CFTs in various dimensions and coupling regimes.

Abstract

We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories around generalised free fields. For theories with higher spin symmetry we discuss the relation between twist conformal blocks and higher spin conformal blocks.