Quantum contribution to domain wall tension from spectral methods

In field theory, domain walls are constructed by embedding localized field configurations varying in one space dimension, such as the $\phi^4$ kink, in two or three space dimensions. At the classical level, the kink mass straightforwardly turns into the energy per unit length or area, known as the domain wall tension. The quantum contribution to the tension is more difficult to compute, because the quantum fluctuations about the domain wall in the additional coordinates must be included. We show that spectral methods, making use of scattering data for the interaction of quantum fluctuations with the domain wall background, are an efficient way to compute the leading quantum correction to the domain wall tension. In particular we demonstrate that within this approach it is straightforward to pass from one renormalization scheme to another.