Abstract
There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar mathcal{N} = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.
Highlights
Scattering amplitudes are one of the most fundamental observables in modern high-energy physics
We study what singularities and branch cuts can appear in integrated Maximal Helicity Violating (MHV) amplitudes at all loop orders in N = 4 planar super Yang-Mills
We show how the boundary structure of the positive kinematic region can be systematically studied using scattering diagrams and find that algebraic letters naturally emerge from the notion of asymptotic chambers in the scattering diagram
Summary
Scattering amplitudes are one of the most fundamental observables in modern high-energy physics. By studying the boundary structure of the positive kinematic region, one can make predictions for what branch points can appear at any loop order [33]. Foremost among these features is the appearance of algebraic letters in the symbol alphabet [36,37,38] To approach these questions, we use scattering diagrams2 [39,40,41,42,43,44], a natural generalization of the cluster algebra framework, to study different compactifications of the positive kinematic region of the 8-point MHV amplitude. We show how the boundary structure of the positive kinematic region can be systematically studied using scattering diagrams and find that algebraic letters naturally emerge from the notion of asymptotic chambers in the scattering diagram. We take an important step towards this goal by proposing a minimal symbol alphabet for algebraic letters
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