The Domain Wall Soliton's Tension

TL;DR

This paper computes the one-loop tension of domain wall solitons in the $^4$ model across 1+1, 2+1, and 3+1 dimensions, confirming previous results and providing new corrections with renormalization details.

Contribution

It presents a new calculation of the one-loop tension correction in 3+1 dimensions, including renormalization procedures for ultraviolet divergences.

Findings

Confirmed previous one-loop tension results in lower dimensions.

Provided a new tension correction of 0.0410959m^3 in 3+1d.

Addressed renormalization of divergences in higher dimensions.

Abstract

We calculate the one-loop tension of the domain wall soliton in the $\phi^4$ 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 $0.0410959m^3$ 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.