arXiv 2403.140622024-03hep-th

单圈阶的(2+1)维畴壁

A (2+1)-Dimensional Domain Wall at One-Loop

Jarah Evslin, Kehinde Ogundipe, Baiyang Zhang, Hengyuan Guo

备注：: 21 pages, 1figure

AI总结：

针对(2+1)维$\u03d5^4$双势阱模型的畴壁，在$O(\u03bb^0)$阶完成量子化，解析推导并数值计算出张力领头阶量子修正为$-0.0866m^2$，验证了Jaimunga等人的结果，还得到激发谱与其他标量模型畴壁单圈张力的通用表达式。

摘要：

我们研究(2+1)维$\boldsymbol{\u03d5^4}$双势阱模型中的畴壁，该畴壁通过将$\u03d5^4$扭结沿额外的无穷维方向延伸而形成。经典情形下，畴壁张力为$m^3/3\u03bb$，其中$\u03bb$为耦合常数，$m$为介子质量。在$\boldsymbol{O(\u03bb^0)}$阶，所有紫外发散均可通过正规序消除，更复杂的发散仅在更高阶才会出现，这使得我们能够在$O(\u03bb^0)$阶轻松对畴壁进行量子化。我们计算了畴壁张力的领头阶量子修正，其形式为对一个解析确定的函数的二维积分。该积分通过数值计算得到结果为$\boldsymbol{-0.0866m^2}$。该修正此前在文献中已有两次计算，但两次结果不一致。我们的结果与Jaimunga、Semenoff和Zarembo的结果一致，从而证实了后者的结论。此外，我们还在该阶得到了畴壁的激发谱，以及其他标量模型中畴壁单圈张力的通用表达式。

英文摘要：

We consider the domain wall in the (2+1)-dimensional $ϕ^4$ double well model, created by extending the $ϕ^4$ kink in an additional infinite direction. Classically, the tension is $m^3/3λ$ where $λ$ is the coupling and $m$ is the meson mass. At order $O(λ^0)$ 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 $O(λ^0)$. 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.

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摘要：

英文摘要：

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