Conical Twist Fields and Null Polygonal Wilson Loops

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.

35 pages, 16 figures. Small typos corrected in v2

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Gluon scattering amplitudes at strong coupling
• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement hamiltonians in two-dimensional conformal field theory
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• On the collinear limit of scattering amplitudes at strong coupling
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• String field theory vertex from integrability
• Form factors of boundary exponential operators in the sinh-Gordon model
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes

Cited by in corpus (9)

• Fluctuations in ballistic transport from Euler hydrodynamics
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Metagroups and their smashed twisted wreath products
• Left invariant measures on locally compact fan loops
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• On structure of topological metagroups
• Smashed products of topological left quasigroups