On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models
High Energy Physics - Theory
2017-09-13 v2
Abstract
We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) -models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.
Cite
@article{arxiv.1706.05221,
title = {On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models},
author = {Ines Aniceto and Zoltan Bajnok and Tamas Gombor and Minkyoo Kim and Laszlo Palla},
journal= {arXiv preprint arXiv:1706.05221},
year = {2017}
}
Comments
Dedicated to the memory of Petr Kulish, 31 pages, 1 figure, v2: conformality and integrability of the boundary conditions are distinguished