无奇点非线性σ模型中的广义对称性及其无序相
Generalized symmetries in singularity-free nonlinear $σ$ models and their disordered phases
AI总结：
本文研究无奇点非线性σ模型的涌现非可逆高形式对称性，通过Postnikov阶段构造d-群G^(d)，证明其无序相由高形式规范理论描述，并以(3+1)维S^2模型为例展示无序相由轴子电动力学描述。
摘要：
我们研究了具有连通目标空间K的(d+1)维时空中的非线性σ模型，并证明在低于奇异场构型（如涡旋）的能量尺度下，它具有涌现的非可逆高形式对称性。该涌现对称性的对称性缺陷由离散d-群G^(d)的d-表示描述（即涌现对称性是可逆d-群G^(d)对称性的对偶）。d-群G^(d)的确定方式为：其分类空间BG^(d)由K的第d个Postnikov阶段给出。在(2+1)维且G^(2)为有限群的情况下，该对称性总是全纯等价于一个具有潜在't Hooft反常的可逆0-形式（普通）对称性。非线性σ模型的无奇点无序相自发破缺该对称性，且当G^(d)为有限群时，该无序相由G^(d)高形式规范理论的解禁闭相描述。我们考虑了此类无序相的若干例子。我们重点研究(3+1)维中的无奇点S^2非线性σ模型，并证明它具有涌现的非可逆高形式对称性。因此，其无序相由轴子电动力学描述，并具有两个无能隙模式，分别对应一个光子和一个无质量轴子。值得注意的是，这一非微扰结果不同于在大N极限下使用S^N和CP^{N-1}非线性σ模型所得到的结果。
英文摘要：
We study the nonlinear $σ$-model in ${(d+1)}$-dimensional spacetime with connected target space $K$ and show that, at energy scales below singular field configurations (such as vortices), it has an emergent non-invertible higher symmetry. The symmetry defects of the emergent symmetry are described by the $d$-representations of a discrete $d$-group $\mathbb{G}^{(d)}$ (i.e. the emergent symmetry is the dual of the invertible $d$-group $\mathbb{G}^{(d)}$ symmetry). The $d$-group $\mathbb{G}^{(d)}$ is determined such that its classifying space $B\mathbb{G}^{(d)}$ is given by the $d$-th Postnikov stage of $K$. In $(2+1)$D and for finite $\mathbb{G}^{(2)}$, this symmetry is always holo-equivalent to an invertible ${0}$-form (ordinary) symmetry with potential 't Hooft anomaly. The singularity-free disordered phase of the nonlinear $σ$-model spontaneously breaks this symmetry, and when $\mathbb{G}^{(d)}$ is finite, it is described by the deconfined phase of $\mathbb{G}^{(d)}$ higher gauge theory. We consider examples of such disordered phases. We focus on a singularity-free $S^2$ nonlinear $σ$-model in ${(3+1)}$D and show that it has an emergent non-invertible higher symmetry. As a result, its disordered phase is described by axion electrodynamics and has two gapless modes corresponding to a photon and a massless axion. Notably, this non-perturbative result is different from the results obtained using the $S^N$ and $\mathbb{C}P^{N-1}$ nonlinear $σ$-models in the large-$N$ limit.
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