Large Spin Perturbation Theory for Conformal Field Theories.

Author: 

Alday, L

Publication Date: 

12 September 2017

Journal: 

Physical review letters

Last Updated: 

2020-07-01T06:49:45.253+01:00

Issue: 

11

Volume: 

119

DOI: 

10.1103/physrevlett.119.111601

page: 

111601-111601

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 generalized 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 generalized free fields.

Symplectic id: 

730919

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article