arXiv subjects

Rebecca Bristow

Publications and source records attributed to Rebecca Bristow.

2 recordsLinked to original sources

arXiv2017

Integrability of generalised type II defects in affine Toda field theory

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.

hep-th↗

arXiv2017

Momentum conserving defects in affine Toda field theories

Type 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 existence of a conserved momentum in the presence of the defect. In addition it is shown that for any Lagrangian satisfying this condition, the defect equations of motion, when taken to hold everywhere, can be extended to give a Bäcklund transformation between the bulk theories on either side of the defect. This strongly suggests that such systems are integrable. Momentum conserving defects and Bäcklund transformations for affine Toda field theories based on the $A_n$, $B_n$, $C_n$ and $D_n$ series of Lie algebras are found. The defect associated with the $D_4$ affine Toda field theory is examined in more detail. In particular classical time delays for solitons passing through the defect are calculated.

hep-th↗