Large Spin Perturbation Theory

TL;DR

This paper develops a systematic method using twist conformal blocks to analyze conformal field theories near points of large twist degeneracy, enabling algebraic solutions to crossing symmetry and spectrum computations.

Contribution

It introduces twist conformal blocks as eigenfunctions of quartic operators and provides a systematic decomposition method for perturbations around degenerate points in conformal field theories.

Findings

Decomposition of four-point correlators into twist conformal blocks simplifies crossing symmetry.

Application of the method to compute spectra around generalized free fields.

Connection established between twist conformal blocks and higher spin conformal blocks.

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.