The domain wall soliton’s tension

Abstract

Abstract We calculate the one-loop tension of the domain wall soliton in the $$\phi ^4$$ ϕ 4 double-well model. Our result agrees with previous results from Dashen, Hasslacher and Neveu (1974) in 1 + 1d and Jaimunga, Semenoff and Zarembo (1999) in 2 + 1d. After an additional 25 year interval, we have obtained a one-loop tension correction of $$0.0410959m^3$$ 0.0410959 m 3 in 3 + 1d. In this case, unlike lower-dimensional cases, even after normal ordering there are ultraviolet divergences that require both mass and also coupling constant renormalization. We renormalized the coupling so that the three-point interaction in the effective potential is given by its tree level value at zero external momenta.