Solvable self-dual impurity models

Abstract

We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS solutions depend on the actual position on moduli space. These results are obtained both for the nontrivial topological sector (kinks or antikinks) as well as for the topologically trivial sector, where the motion on moduli space represents a kink-antikink annihilation process.

sec. 6.1 corrected

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• Complex BPS solitons with real energies from duality
• Supersymmetric Inhomogeneous Field Theories in 1+1 Dimensions
• Collisions between kinks with long-range tails: a simple and efficient method
• A Reduced Inner Product for Kink States
• Maxwell-scalar system and scalar field with impurity: novel approach to find nontrivial solutions
• Compact-like vortices in isotropic curved spacetime
• Background fields and self-dual Skyrmions
• Constrained instantons and kink-antikink collisions
• Phonons scattering off discrete asymmetric solitons in the absence of a Peierls-Nabarro potential
• Highly-enhanced propagation of long-range kinks in heterogeneous media
• Scalar fields with impurities in arbitrary dimensions: first-order framework and exact solutions
• Moduli space with a boundary
• Bogomolny equations for the BPS Skyrme models with impurity
• Generalized scalar field models in the presence of impurities
• BPS deformations of the Skyrme model
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