To see Symmetry in a Forest of Trees

TL;DR

This paper re-examines exact symmetry identities in bosonic open string theory, introducing new kinematic configurations and polarization bases to simplify the analysis and connect high-energy symmetries with exact identities.

Contribution

It provides explicit constructions of kinematic setups and polarization bases, facilitating the extraction of high-energy limits and linking stringy symmetries to known high-energy behaviors.

Findings

Simplified functional forms of symmetry identities

Explicit high-energy limits of string amplitudes

Connections between exact and high-energy string symmetries

Abstract

The exact symmetry identities among four-point tree-level amplitudes of bosonic open string theory as derived by G. W. Moore are re-examined. The main focuses of this work are: (1) Explicit construction of kinematic configurations and a new polarization basis for the scattering processes. These setups simplify greatly the functional forms of the exact symmetry identities, and help us to extract easily high-energy limits of stringy amplitudes appearing in the exact identities. (2) Connection and comparison between D. J. Gross's high-energy stringy symmetry and the exact symmetry identities as derived by G. W. Moore. (3) Observation of symmetry patterns of stringy amplitudes with respect to the order of energy dependence in scattering amplitudes.