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A (2+1)-Dimensional Domain Wall at One-Loop
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abstract
We consider the domain wall in the (2+1)-dimensional $\phi^4$ double well model, created by extending the $\phi^4$ kink in an additional infinite direction. Classically, the tension is $m^3/3\lambda$ where $\lambda$ is the coupling and $m$ is the meson mass. At order $O(\lambda^0)$ all ultraviolet divergences can be removed by normal ordering, less trivial divergences arrive only at the next order. This allows us to easily quantize the domain wall, working at order $O(\lambda^0)$. We calculate the leading quantum correction to its tension as a two-dimensional integral over a function which is determined analytically. This integral is performed numerically, resulting in $-0.0866m^2$. This correction has previously been computed twice in the literature, and the results of these two computations disagreed. Our result agrees with and so confirms that of Jaimunga, Semenoff and Zarembo. We also find, at this order, the excitation spectrum and a general expression for the one-loop tensions of domain walls in other scalar models.
Forward citations
Cited by 6 Pith papers
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Effective Actions for Domain Wall Dynamics
The effective action for domain walls, including higher-curvature corrections and a bound-state coupling to worldsheet curvature, is derived from the scalar field theory and matched to lattice simulations.
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An Extended Soliton's Zero Modes
For infinitely extended solitons the translation zero mode can be given a normalizable wave function, and the resulting Stokes scattering probability for exciting a string's translation mode is computed.
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The Domain Wall String's Anti-Stokes Scattering Cross Section
The authors compute the anti-Stokes scattering cross section for a domain wall string shape mode in a scalar theory, yielding a wave-packet-independent analytic formula for arbitrary incident angle and impact parameter.
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The Domain Wall Soliton's Tension
The one-loop domain wall tension in 3+1d phi^4 theory is computed as m^3/(3λ) + 0.0410959 m^3 under a chosen renormalization scheme.
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Constructing A Finite Tension Domain Wall in $\phi^4_4$
The one-loop domain wall tension in φ^4_4 is finite because the positive divergence from the displacement operator is exactly cancelled by the negative divergence from the squeeze (Bogoliubov) contribution.
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(Anti-)Stokes Scattering on the Domain Wall String
Meson scattering off a (2+1)-dimensional domain wall string can excite or de-excite the string's shape mode, and this paper gives the leading-order probability densities for both processes, including forward and backw...
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