On a_2^(1) Reflection Matrices and Affine Toda Theories

TL;DR

This paper constructs new reflection matrices for affine Toda theories with quantum affine symmetry, providing explicit solutions, scalar factors, and conjectured reflection factors for fundamental particles, linking quantum and classical results.

Contribution

It introduces novel non-diagonal solutions to the boundary Yang-Baxter equation for a_2^(1) affine Toda theories, including scalar factors and reflection factors for bound states.

Findings

Derived new boundary reflection matrices satisfying unitarity and crossing symmetry.

Computed reflection factors for scalar bound states (breathers).

Proposed conjectured reflection factors for fundamental particles in affine Toda theory.

Abstract

We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary crossing symmetry are then used to find overall scalar factors which lead to consistent reflection matrices. Using the boundary bootstrap equations we also compute the reflection factors for scalar bound states (breathers). These breathers are expected to be identified with the fundamental quantum particles in a_2^(1) affine Toda field theory and we therefore obtain a conjecture for the affine Toda reflection factors. We compare these factors with known classical results and discuss their duality properties and their connections with particular boundary conditions.