AI 中文总结
研究引入半对偶化构建不可逆对偶缺陷，在(2 + 1)维Villain化电荷 - $n$ XY模型及相关$\mathbb{Z}_n$规范XY模型中演示，产生不可逆粒子 - 涡旋对偶缺陷等，还表明规范模型中半对偶化界面情况及红外流向。
AI 中文摘要
我们引入半对偶化作为构建不可逆对偶缺陷的一般原理。该构建仅在时空的一个子区域执行对偶变换，在原理论与其对偶之间留下一个界面，不可逆对偶缺陷可存在于此界面上。半对偶化适用于任何有局部对偶变换的情况，且不依赖于时空维度。我们在立方晶格上的(2 + 1)维Villain化电荷 - $n$ XY模型中演示了构建过程，半对偶化产生了一个不可逆粒子 - 涡旋对偶缺陷，其与取向相反的缺陷融合在融合面上产生一个(1 + 1)维$\mathbb{Z}_n$规范理论。然后我们将半对偶化应用于与3D XY$^\ast$转变相关的$\mathbb{Z}_n$规范XY模型，在规范模型中，半对偶化界面存在一个规范协变对偶壁，而非真正的规范不变对偶缺陷，当$\mathbb{Z}_n$规范理论被限制或希格斯化时，它在红外区域流向一个可逆对偶缺陷。
英文摘要
We introduce half dualization as a general principle to construct non-invertible duality defects. The construction performs a duality transformation only in a subregion of spacetime, leaving an interface between the original theory and its dual. A non-invertible duality defect can be hosted on this interface. Half dualization is applicable whenever a local duality transformation is available, and does not depend on the spacetime dimension. We demonstrate the construction procedure in the (2+1)-dimensional Villainized charge-$n$ XY model on a cubic lattice. Half dualization yields a non-invertible particle-vortex duality defect whose fusion with its orientation reverse produces a (1+1)-dimensional $\mathbb{Z}_n$ gauge theory on the fusion surface. We then apply half dualization to the $\mathbb{Z}_n$-gauged XY model relevant to the 3D XY$^\ast$ transition. In the gauged model, the half dualization interface hosts a gauge covariant duality wall, rather than a genuine gauge invariant duality defect. It flows to an invertible duality defect in infrared when the $\mathbb{Z}_n$ gauge theory is confined or Higgsed.
Comments6.5 pages
