Adam, ChristophOles, K.Fernández Queiruga, José ManuelRomanczukiewicz, T.Wereszczynski, Andrzej2020-04-142020-04-142019Adam, C., Oles, K., Queiruga, J. et al. Solvable self-dual impurity models. J. High Energ. Phys. 2019, 150 (2019). https://doi.org/10.1007/JHEP07(2019)150http://hdl.handle.net/10347/21406We 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 processeng© The Authors 2019. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are creditedhttps://creativecommons.org/licenses/by/4.0/Nonperturbative effectsSolitons monopoles and instantonsEffective field theoriesjournal article10.1007/JHEP07(2019)1501029-8479open access