Sigma models in the presence of dynamical point-like defects

Abstract

Point-like Liouville integrable dynamical defects are introduced in the context of the Landau-Lifshitz and Principal Chiral (Faddeev-Reshetikhin) models. Based primarily on the underlying quadratic algebra we identify the first local integrals of motion, the associated Lax pairs as well as the relevant sewing conditions around the defect point. The involution of the integrals of motion is shown taking into account the sewing conditions.Comment: 19 pages, Latex; Clarifications and references added; Published versio

Type-II defects in the super-Liouville theory

“…The study of two-dimensional integrable field theories in the presence of defects or impurities has evolved into a rich subject in recent years from both classical and quantum points of view [1]- [14]. The Lagrangian formalism was initially introduced in [3] to describe integrable defect conditions through a suitable local Lagrangian density located at a fixed point.…”

Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations

“…Several other interesting issues have been studied for these types of integrable defects, among which the following are worth mentioning: the computation of the higher order modified conserved quantities and their involutivity [9,10,11], quantum description [12,13,14,15,16,17,18,19,20] (see also [21,22] for the discussion of soliton defects in quantum systems), the multisimplectic description [23,24,25,26], finite-gap solutions [27], extensions for non-simply laced affine Toda models [28,29,30,31], and fermionic [32,33,34] and supersymmetric extensions [35,36,37,38,39].…”

N=1 super sinh-Gordon model with defects revisited

“…On the other hand, the question of involutivity of the modified conserved charges has been addressed for several models [8]- [11], by using essentially the algebraic framework of the classical r-matrix approach, and a modified transition matrix to describe integrable defects.…”