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arXiv 1911.03494hep-th
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纯二维Yang-Mills理论中的自发对称性破缺

Spontaneous symmetry breaking in pure 2D Yang-Mills theory

Gleb Aminov

备注：
The ambiguity between the second Stiefel-Whitney class $w_2$ and an invariant of $PSU(N)$ bundles $u_2$ was removed. Conclusion section and more references were added in version 3
发表信息：
Phys. Rev. D 101, 105017 (2020)
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摘要：

我们考虑环面上的纯拓扑$2$ d Yang-Mills理论，其中第二个Stiefel-Whitney类以$θ$ -项的形式加到拉格朗日量上.我们将证明，在$θ=π$存在一类具有二重简并真空的$SU(2 N)/\mathbb{Z}_2$（$N>1$）规范理论，它自发地破坏了时间反演和电荷共轭对称性。相应的序参量由$\mathbb{Z}_N$的生成元$\mathcal{O}$给出。

英文摘要：

We consider purely topological $2$d Yang-Mills theory on a torus with the second Stiefel-Whitney class added to the Lagrangian in the form of a $θ$-term. It will be shown, that at $θ=π$ there exists a class of $SU(2 N)/\mathbb{Z}_2$ ($N>1$) gauge theories with a two-fold degenerate vacuum, which spontaneously breaks the time reversal and charge conjugation symmetries. The corresponding order parameter is given by the generator $\mathcal{O}$ of the $\mathbb{Z}_N$ one-form symmetry.

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