Conical Twist Fields and Null Polygonal Wilson Loops

TL;DR

This paper introduces conical twist fields in 2D integrable quantum field theories, revealing their unique properties and potential relevance to understanding null polygonal Wilson loops and gluon scattering amplitudes in supersymmetric Yang-Mills theory.

Contribution

It extends the concept of twist fields to space-time symmetries, characterizes their properties, and proposes their application to gauge theory observables.

Findings

Conical twist fields have the same conformal dimension as branch-point twist fields.

They generate different operator product expansions and form factor expansions.

Resummation of form factors confirms the correctness of their operator product expansions.

Abstract

Using an extension of the concept of twist field in QFT to space-time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon appropriate identification between the excess angle and the number of sheets, they have the same conformal dimension as branch-point twist fields commonly used to represent partition functions on Riemann surfaces, and that both fields have closely related form factors. However, we show that conical twist fields are truly different from branch-point twist fields. They generate different operator product expansions (short distance expansions) and form factor expansions (large distance expansions). In fact, we verify in free field theories, by re-summing form factors, that the conical twist fields operator product expansions are correctly reproduced. We propose that conical twist fields are the correct fields in order to understand null polygonal Wilson loops/gluon scattering amplitudes of planar maximally supersymmetric Yang-Mills theory.