Folding defect affine Toda field theories

Abstract

A folding process is applied to fused a (1) r defects to construct defects for the non-simply laced affine Toda field theories of cn and a (2) 2n at the classical level. Support for the hypothesis that these defects are integrable in the folded theories is given by the demonstration that energy and momentum are conserved. Further support is provided by the observation that transmitted solitons retain their form.

Integrability of generalised type II defects in affine Toda field theory

“…These defects with auxiliary fields are referred to as type II defects. This idea of extra fields at the defect, and JHEP11(2017)067 the fact that one ATFT can be folded to a different ATFT using certain symmetries of the Dynkin diagram [29,30], was used in [7] to fold existing A r ATFT defects to new C r ATFT defects. These type II defects were generalised in [1] and momentum conserving defects were found in the B r and D r ATFTs.…”

“…This Lagrangian set-up was pioneered in [2]. Motivated by the form of the type I defects appearing in [2][3][4][5] and the type II defects appearing in [6,7] the generalised type II defect Lagrangian density was taken to be…”

“…A defect is some discontinuity in physical media or fields in a mathematical model, and we will check whether incorporating a discontinuity into an integrable model can be achieved without destroying its integrability. We follow the classical Lagrangian picture of defects introduced in [2] and further studied in [1,[3][4][5][6][7][8]. In this approach for a defect at x = 0 there is a field vector u defined in the region x ≤ 0 and a field vector v defined in the region x ≥ 0, with both fields obeying the same bulk theory.…”

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].…”

Type II defects revisited

“…So far, there are basically two types of defect that appear to be integrable, called type I (where the defect has no degrees of freedom of its own [4,5]), and type II (where the defect carries its own degrees of freedom [12,17]). However, they can be mixed together as they have been recently, for example, to discuss defects within the d (1) r series of affine Toda field theories [18].…”