Open Spin Chains and Complexity in the High Energy Limit

TL;DR

This paper explores the integrability of open spin chains in high energy scattering amplitudes, revealing new insights into the complexity and scaling laws in quantum chromodynamics and supersymmetric theories.

Contribution

It introduces the concept of complexity in high energy effective field theory and analyzes the scaling laws of open spin chains in this context.

Findings

Identification of complexity scaling laws in high energy spin chains

Connection between open spin chains and high energy scattering amplitudes

Insights into integrability in quantum chromodynamics and supersymmetric theories

Abstract

In the high energy limit of scattering amplitudes in Quantum Chromodynamics and supersymmetric theories the dominant Feynman diagrams are characterized by a hidden integrability. A well-known example is that of Odderon exchange, which can be described as a bound state of three reggeized gluons and corresponds to a closed spin chain with periodic boundary conditions. In the $N=4$ supersymmetric Yang-Mills theory a similar spin chain arises in the multi-Regge asymptotics of the eight-point amplitude in the planar limit. We investigate the associated open spin chain in transverse momentum and rapidity variables solving the corresponding effective Feynman diagrams. We introduce the concept of complexity in the high energy effective field theory and study its emerging scaling laws.