Abstract
Plahte identities are monodromy relations between open string scattering amplitudes at tree level derived from the Koba-Nielsen formula. We represent these identities by polygons in the complex plane. These diagrams make manifest the appearance of sign changes and singularities in the analytic continuation of amplitudes. They provide a geometric expression of the KLT relations between closed and open string amplitudes. We also connect the diagrams to the BCFW on-shell recursion relations and generalise them to complex momenta resulting in a relation between the complex phases of partial amplitudes.
Highlights
Congruence with the field theory of pure Yang-Mills amplitudes where one can use KleissKujif relations and BCJ relations to represent all color-ordered gauge amplitudes in terms of a basis (n − 3)! amplitudes
We show how the identities can be used to illustrate the analytic continuation of the Koba Nielsen formula, which requires us to discuss how these Plahte diagrams are modified when amplitudes become negative and when they diverge
We have investigated geometrical diagrams based on linear monodromy relations between open string amplitudes discovered by Plahte
Summary
First described by Plahte [2], Plahte identities are monodromy relations between partial open string scattering amplitudes. The Plahte identities (A.4) for n particle scattering can be depicted by nsided polygons in the complex plane whose sides are given by colour-ordered open string amplitudes and its angles correspond to products of two momenta. We need to emphasise that in all the Plahte diagrams we constructed we took the partial amplitudes to be real, positive and finite This is not true for general kinematics as the amplitudes have to be defined by analytic continuation and it is possible for open string amplitudes to be negative or even divergent. We will discuss more of these aspects
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