Integrability of generalised type II defects in affine Toda field theory

Abstract

The Liouville integrability of the generalised type II defects is investigated. Full integrability is not considered, only the existence of an infinite number of conserved quantities associated with a system containing a defect. For defects in affine Toda field theories (ATFTs) it is shown that momentum conservation is very likely to be a necessary condition for integrability. The defect Lax matrices which guarantee zero curvature, and so an infinite number of conserved quantities, are calculated for the momentum conserving Tzitzéica defect and the momentum conserving D 4 ATFT defect. Some additional calculations pertaining to the D 4 defect are also carried out to find a more complete set of defect potentials than has appeared previously.

Quantum anomalies in A(1) r Toda theories with defects

“…More recently type-II line defects, i.e. defects with additional degrees of freedom λ propagating on them, have been investigated from a classical point of view [52][53][54][55][56]. It has been argued that a larger class of integrable theories seem to survive the presence of this kind of more general impurities.…”

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].…”