Boundary Reflection Matrix for $D_4^{(1)}$ Affine Toda Field Theory

TL;DR

This paper derives the one-loop boundary reflection matrix for the $d_4^{(1)}$ Toda field theory with Neumann boundary conditions, revealing cancellations and proposing a unique, non-minimal exact boundary reflection matrix consistent with duality.

Contribution

It provides the first explicit one-loop boundary reflection matrix for $d_4^{(1)}$ Toda theory and determines the exact boundary reflection matrix considering duality.

Findings

Non-meromorphic terms cancel at one-loop level.

Exact boundary reflection matrix is uniquely determined.

The reflection matrix is non-minimal under duality assumptions.

Abstract

We present one loop boundary reflection matrix for $d_4^{(1)}$ Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when the model has a particle spectrum with more than one mass. Using this result, we determine uniquely the exact boundary reflection matrix which turns out to be \lq non-minimal' if we assume the strong-weak coupling \lq duality'.