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Conical Twist Fields and Null Polygonal Wilson Loops

Research output: Contribution to journalArticlepeer-review

Olalla A. Castro-Alvaredo, Benjamin Doyon, Davide Fioravanti

Original languageEnglish
Pages (from-to)146-178
JournalNuclear Physics, Section B
Early online date11 Apr 2018
Accepted/In press5 Apr 2018
E-pub ahead of print11 Apr 2018
PublishedJun 2018


King's Authors


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.

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