Square Root Singularity in Boundary Reflection Matrix

TL;DR

This paper conjectures a new type of square root singularity in the boundary reflection matrix for affine Toda field theory with Neumann boundary conditions, challenging the usual pole-zero singularity structure.

Contribution

It introduces a novel square root singularity in boundary reflection matrices, supported by one-loop calculations, for affine Toda field theories with twisted affine algebras.

Findings

Conjecture of square root singularity in boundary reflection matrices.

Support from one-loop computational results.

Implication for the structure of scattering amplitudes in integrable models.

Abstract

Two-particle scattering amplitudes for integrable relativistic quantum field theory in 1+1 dimensions can normally have at most singularities of poles and zeros along the imaginary axis in the complex rapidity plane. It has been supposed that single particle amplitudes of the exact boundary reflection matrix exhibit the same structure. In this paper, single particle amplitudes of the exact boundary reflection matrix corresponding to the Neumann boundary condition for affine Toda field theory associated with twisted affine algebras $a_{2n}^{(2)}$ are conjectured, based on one-loop result, as having a new kind of square root singularity.