On the effects of irrelevant boundary scaling operators

TL;DR

This paper studies how adding irrelevant boundary operators affects (1+1)-dimensional field theories, showing that low-energy behavior remains stable while high-energy behavior can vary, with implications for integrable and non-integrable models.

Contribution

It demonstrates that irrelevant boundary operators modify reflection matrices via CDD factors in integrable models and shows IR stability in non-integrable models through Monte Carlo simulations.

Findings

Irrelevant boundary operators multiply reflection matrices by CDD factors.

Low-energy behavior remains unchanged despite irrelevant perturbations.

High-energy behavior can exhibit roaming RG trajectories.

Abstract

We investigate consequences of adding irrelevant (or less relevant) boundary operators to a (1+1)-dimensional field theory, using the Ising and the boundary sine-Gordon model as examples. In the integrable case, irrelevant perturbations are shown to multiply reflection matrices by CDD factors: the low-energy behavior is not changed, while various high-energy behaviors are possible, including ``roaming'' RG trajectories. In the non-integrable case, a Monte Carlo study shows that the IR behavior is again generically unchanged, provided scaling variables are appropriately renormalized.