# Twisting perturbed parafermions

## TL;DR

This paper develops a formalism for analyzing twist operators in perturbed sigma models related to scattering amplitudes in supersymmetric Yang-Mills theory, using conformal perturbation theory and parafermions.

## Contribution

It introduces a novel approach to compute properties of twist operators in perturbed sigma models via conformal symmetry and parafermionic reformulation.

## Key findings

- Reformulation of the O(3) sigma model as perturbed parafermions.
- Application of conformal perturbation theory to twist operators.
- Framework for systematic calculations in related models.

## Abstract

The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang-Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6) nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current-current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3) sigma model which is reformulated as perturbed parafermions.