Background field boundary conditions for affine Toda field theories

TL;DR

This paper explores how classical integrability of affine Toda field theories is affected by constant background tensor fields, revealing new discrete boundary conditions dependent on the fields' time-derivatives at the boundary.

Contribution

It introduces a novel set of boundary conditions for affine Toda field theories influenced by background tensor fields, expanding the understanding of integrable boundary scenarios.

Findings

Discrete boundary conditions depend on the time-derivative of fields

Boundary conditions contain no free parameters besides the bulk coupling

New integrability conditions are identified in the presence of background fields

Abstract

Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable boundary conditions depending upon the time-derivative of the fields at the boundary but containing no free parameters other than the bulk coupling constant.