Boundary Lax pairs for the $A_{n}^{(1)}$ Toda field theories

Details Boundary Lax pairs for the $A_{n}^{(1)}$ Toda field theories Boundary Lax pairs for the $A_{n}^{(1)}$ Toda field theories

2008-09-16

arxiv.org/abs/0809.2734v3

Nucl.Phys.B821:481-505,2009

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, Latex. Typos corrected, clarifications added. Version to appear in NBP

Scientific paper

10.1016/j.nuclphysb.2009.05.010

Based on the recent formulation of a general scheme to construct boundary Lax pairs,we develop this systematic construction for the $A_n^{(1)}$ affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sine-Gordon ($A_1^{(1)}$) and the $A_2^{(1)}$ models. The $A_2^{(1)}$ Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.

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