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Summary
The paper calculates the one-loop tension of the domain wall soliton in the ϕ4 double-well model, obtaining a correction of 0.0410959m3 in 3+1 dimensions.
Highlights
- The authors use linearized soliton perturbation theory (LSPT) to compute the one-loop correction to the domain wall tension.
- The result agrees with previous calculations in 1+1 and 2+1 dimensions.
- In 3+1 dimensions, ultraviolet divergences require both mass and coupling constant renormalization.
- The authors use a Heisenberg picture renormalization scheme, fixing counterterms by demanding that higher-order corrections to the effective action vanish.
- The domain wall tension is calculated using a cylindrical coordinate system, which respects the symmetries of the domain wall.
- The continuum contribution to the tension is infinite but is canceled by the scheme-dependent contribution from the counterterms.
- The final result for the tension is ρ ∼ m3/(3λ) + 0.0410959m3 + O(m3λ).
Key Insights
- The LSPT method allows for a straightforward extension to any number of loops and can be applied to form factors, amplitudes, and decay rates, making it a powerful tool for studying quantum solitons.
- The use of Heisenberg picture renormalization simplifies the calculation and avoids the need for a tedious Schrödinger picture renormalization.
- The cylindrical coordinate system is well-suited for the domain wall calculation, as it respects the symmetries of the system and simplifies the integration.
- The infinite continuum contribution to the tension is a result of the logarithmic ultraviolet divergence in the integral, which is canceled by the counterterms.
- The final result for the tension shows a positive correction to the classical tension, which depends on the choice of renormalization conditions.
- The LSPT method can be applied to other models and dimensions, providing a general framework for studying quantum solitons.
- The calculation of the domain wall tension has implications for understanding the interactions of domain walls with radiation and their internal excitations, which are important for phenomenological applications.
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Citation
Evslin, J., Liu, H., & Zhang, B. (2024). The Domain Wall Soliton’s Tension (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20814