# Affine Toda field theories with defects

@article{Bowcock2004AffineTF, title={Affine Toda field theories with defects}, author={Peter Bowcock and Edward Corrigan and C. Zambon}, journal={Journal of High Energy Physics}, year={2004}, volume={2004}, pages={056} }

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 ar(1) 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…

## 78 Citations

### Momentum conserving defects in affine Toda field theories

- Physics
- 2016

A bstractType II integrable defects with more than one degree of freedom at the defect are investigated. A condition on the form of the Lagrangian for such defects is found which ensures the…

### On defects in affine Toda field theory

- Biology
- 2015

This thesis outlines methods for generating new integrable defects in affine Toda field theory. These methods are grounded in the hypothesis that defects have a particle-like classification with as…

### Quantum anomalies in Ar(1) Toda theories with defects

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe study quantum integrability of affine Toda theories with a line of defect. In particular, we focus on the problem of constructing quantum higher-spin conserved currents in models defined…

### Integrability of generalised type II defects in affine Toda field theory

- Mathematics
- 2017

A bstractThe 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…

### Comments on defects in the ar Toda field theories

- Physics
- 2009

A simple, basic argument is given, based solely on energy–momentum considerations, to recover conditions under which ar affine or conformal Toda field theories can support defects of integrable type.…

### On purely transmitting defects in affine Toda field theory

- Physics
- 2007

Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a2 is analysed in detail. After providing a complete characterization of the problem in a…

### ON A SYSTEMATIC APPROACH TO DEFECTS IN CLASSICAL INTEGRABLE FIELD THEORIES

- Mathematics
- 2008

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of…

### Folding defect affine Toda field theories

- Physics
- 2014

A folding process is applied to fused ar(1)?> defects to construct defects for the non-simply laced affine Toda field theories of cn(1)?>, dn(2)?> and a2n(2)?> at the classical level. Support for the…

## References

SHOWING 1-10 OF 26 REFERENCES

### Classically integrable field theories with defects

- Mathematics
- 2003

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example…

### Local conserved densities and zero-curvature conditions for Toda lattice field theories

- Mathematics
- 1985

### On the topological charges of the affine toda solitons

- Physics
- 1994

This thesis investigates the two dimensional, integrable field theories known as the affine Toda field theories, which are based on the Kac-Moody algebras with zero central extension. In particular,…

### Recent Developments in Affine Toda Quantum Field Theory

- Physics
- 1999

It is not intended to give a detailed review of all the recent activities in the area of Toda field theory, but rather to highlight some of the interesting developments, and to point out some of the…

### Quantum corrections to the classical reflection factor of the sinh-Gordon model

- Mathematics
- 2000

This thesis studies the quantum reflection factor of the sinh-Gordon model under boundary conditions consistent with integrability. First, we review the affine Toda field theory in Chapter One. In…

### Coupling integrable field theories to mechanical systems at the boundary

- Physics, Mathematics
- 2001

We present an integrable Hamiltonian which describes the sinh-Gordon model on the half line coupled to a non-linear oscillator at the boundary. We explain how we apply Sklyanin's formalism to a…