论文标题
仪表理论地理：绘制半经典岛之间的路径
Gauge theory geography: charting a path between semiclassical islands
论文作者
论文摘要
我们研究$ su（2）$ yang-mills理论的两个半古老限制，上面有“ hoft twist：t hooft twist：``'femtouniverse''，其中所有$ \ mathbb {t}^3 $方向都很小，并且在$ \ \ mathbb {$ \ mathbb {$ {$ {$ {$} $ {2 \ \ \ \ \ \ \ \ times^2 bb \ \ \ \ \ bb { $ \ mathbb {s}^1 $和大或无限$ \ mathbb {t}^2 $。仔细定义对称性，我们表明经典基础状态虽然不同，但在1形中心对称性和平价下具有相同的转换特性。我们认为，这是这些理论的相同多分支$θ$依赖的真空结构的背后。然后，我们计算出$ \ mathbb {s}^1 $ - 霍尔摩利的一环潜力，而在$ \ mathbb {t}^2 $上存在曲折的情况下。我们使用它来研究仪表理论中半经典基础状态的量子稳定性，并在空间$ \ mathbb {t}^2 \ times \ times \ mathbb {s}^1 $上具有巨大或无质量的伴随费，并在$ \ mathbb {t}^2 $中有所不同。结果指出了一些值得进一步研究的有趣特征。
We study two semiclassical limits of $SU(2)$ Yang-Mills theory on a spatial torus with a 't Hooft twist: the ``femtouniverse,'' where all $\mathbb{T}^3$ directions are small, and deformed Yang-Mills theory on $\mathbb{T}^2 \times \mathbb{S}^1$, with small $\mathbb{S}^1$ and large or infinite $\mathbb{T}^2$. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch $θ$-dependent vacuum structure of these theories. We then calculate the one-loop potential for the $\mathbb{S}^1$-holonomy in the presence of twists on $\mathbb{T}^2$. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial $\mathbb{T}^2 \times \mathbb{S}^1$, with a twist in the $\mathbb{T}^2$. The results point towards some interesting features worthy of further study.
