Affine Toda field theories with defects

Abstract

A Lagrangian approach is proposed and developed to study defects within affine Toda field theories. In particular, a suitable Lax pair is constructed together with examples of conserved charges. It is found that only those models based on a (1) r data appear to allow defects preserving integrability. Surprisingly, despite the explicit breaking of Lorentz and translation invariance, modified forms of both energy and momentum are conserved. Some, but apparently not all, of the higher spin conserved charges are also preserved after the addition of contributions from the defect. This fact is illustrated by noting how defects may preserve a modified form of just one of the spin 2 or spin -2 charges but not both of them.

Aspects of sine-Gordon solitons, defects and gates

“…It would also be interesting to investigate further the quantum aspects of field theories with defects (developing ideas originally pioneered by Delfino et al [15]). In the past, the quantum sine-Gordon model has been investigated (see, for example [16]), mostly from an algebraic point of view, but it is not yet clear all the properties outlined above (and those given in references [1,2]) have been properly taken into account. In particular, no mention has been made previously concerning a defect's ability to change topological charge by ±1, although it is clear the transmission matrix discovered by Konik and LeClair does allow transitions between solitons and anti-solitons changing topological charge by ±2.…”

Purely transmitting integrable defects

“…However, there are other solutions too, for example Liouville-Liouville, Liouville-massless free, free-free. In fact, in many cases investigated so far, including cases with several scalar fields [1,5], it turns out that the requirements of integrability coincide with the requirement that there be a modified conserved momentum.…”

Взгляд На Дефекты В Интегрируемой Квантовой Теории Поля

“…Существует много интересных свойств, присущих дефектам в теории синус-Гордон, которые рассматривались другими ис-следователями (см., например, работы [19], [20]), а также дефектам, которые мо-гут возникать в рамках расширений теории синус-Гордон, включая фермионы или анализ взаимосвязи с массивной моделью Тирринга [21], или в рамках других инте-грируемых теорий поля нетодовского типа, таких как НУШ, КдФ или мКдФ [22]. Дефекты можно строить в рамках a (1) r -серии аффинных моделей Тоды [5], а мат-рицы прохождения были выписаны для дефектов как типа I, так и типа II в рабо-тах [6], [13]. Для всех аффинных квантовых групп можно построить обобщенные представления борелевских подалгебр в терминах операторов рождения и уничто-жения [13], хотя имеются альтернативные подходы, которые возникают в других приложениях, например представления Q-оператора Бакстера в контексте решае-мых спиновых цепочек [23].…”

“…• Распространение дефектов типа I на другие теории поля типа аффинной теории Тоды возможно только для моделей, основанных на серии a (1) n [5], [6].…”