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The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced soliton equation in the context of two-dimensional models with kinks. Results include a finite degree of freedom regularization of soliton sector physics based on periodic and anti-periodic lattice models, a detailed analysis of numerical solutions, and the development of perturbation theory in the soliton momentum transfer to mass ratio Delta P/M. Numerical solutions at large transfer Delta P/M are capable of exhibiting, in a smooth and controlled fashion, extreme phenomena such as soliton-antisoliton pair creation and superluminal collective coordinate velocities, which we investigate. 

We answer the question: If a vacuum sector Hamiltonian is regularized by an energy cutoff, how is the one-kink sector Hamiltonian regularized? We find that it is not regularized by an energy cutoff, indeed normal modes of all energies are present in the kink Hamiltonian, but rather the decomposition of the field into normal mode operators yields coefficients which lie on a constrained surface that forces them to become small for energies above the cutoff. This explains the old observation that an energy cutoff of the kink Hamiltonian leads to an incorrect one-loop kink mass. To arrive at our conclusion, we impose that the regularized kink sector Hamiltonian is unitarily equivalent to the regularized vacuum sector Hamiltonian. This condition implies that the two regularized Hamiltonians have the same spectrum and so guarantees that the kink Hamiltonian yields the correct kink mass. 

A bstract Four-dimensional $$ \mathcal{N} $$ N = 4 super Yang-Mills, with a codimension-one defect breaking half of the supersymmetry, arises as the field theory description of the D3/D5 intersection in the holographic limit. This is one of the earliest, most extensively studied, and commonly used systems in holography. In this note we give the full R-symmetry-covariant supersymmetry variations for this system. We also provide the supercurrents and compute the algebra of the corresponding supercharges, obtaining the full set of central charges. We show that magnetically charged finite-energy field configurations preserving half of the supersymmetry are solutions to a new form of the extended Bogomolny equations, in which the defect fields play the role of jumping data for the Nahm-like part of the equations. In the appendices, we explain the connection between our results and the superspace-based formulations in the literature.