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.
Highlights
In quantum field theory (QFT) any singularity in an otherwise flat space–time is associated with a quantum field localized on the singularity
The conical twist field is of a different nature, and does neither require n to be an integer (α to be a multiple of 2π ) nor the model to consist of n replicas
In particular we argue that, unlike the more standard definition of a twist field in QFT as a field associated with an internal symmetry of the theory, conical twist fields are associated with rotational space–time symmetry and insert conical singularities corresponding to excess rotation angle α
Summary
In quantum field theory (QFT) any singularity in an otherwise flat space–time is associated with a quantum field localized on the singularity. With the definition given here of the conical twist field we have set on solid ground the interpretation of the form factor series obtained for gluon scattering amplitudes/null polygonal WLs. The exact interpretation was made in the massless limit of the O(6) NLSM, realised by the infinite ’t Hooft coupling limit. We observe that the form factor resummation becomes subtle when any of the excess angles is negative in which cases a detailed analysis of the integrands’ pole structure is required This is reminiscent of the kind of issues that arise when analytically continuing the correlators of branch point twist fields from n integer to n ≥ 1 and real. A derivation of four defining properties of the conical twist field is presented in appendix A
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