标题： $3$-形式规范理论的全局方面：对横场-杨-米尔斯系统的启示 显示英文标题

标题： Global aspects of $3$-form gauge theory: implications for axion-Yang-Mills systems

摘要： 我们研究了轴子-杨-米尔斯系统在深红外区域可以用一种$3$-形式规范理论来描述的命题。 通过首先开发一个系统的框架来分析耦合到轴子的$3$-形式规范理论，严格检验了这一假设，重点放在其全局性质上。 该理论由受边缘和无关算符变形的BF项组成，并描述了一组由轴子弦交汇处的墙分隔的真空网络。 它包括$0$-形式和$3$-形式自发破缺的全局对称性。 利用这个框架，结合有效场论技术和't Hooft反常匹配条件，我们论证了$3$-形式规范理论忠实地捕捉了轴子-杨-米尔斯系统的红外物理。 紫外理论是一种$SU(N)$非阿贝尔杨-米尔斯理论，带有无质量的狄拉克费米子与一个复标量耦合，并由手征和真正的$\mathbb{Z}_m^{(1)}$ $1$ -形式中心对称性所表征，它们之间存在混合反常。 该理论有两个尺度：复标量的vev（真空期望值）$v$和强耦合尺度$\Lambda$，满足$\Lambda \ll v$。 在下方$v$之下，费米子脱离耦合，出现了一个$U(1)^{(2)}$ $2$ -形式缠绕对称性，而$1$-形式对称性增强到了$\mathbb Z_N^{(1)}$。 当我们流到下方的$\Lambda$时，匹配混合反常需要引入一个动力学的$3$-形式规范场$U(1)^{(2)}$，它表现为色场长程尾的表现形式。 红外理论具有自发破缺的手征和新兴的$3$-形式整体对称性。 它通过了几个检查，其中包括：当真空之间发生转变时，它在强子扇区表现出预期的重组，并且在真正$\mathbb Z_m^{(1)}\subset \mathbb Z_N^{(1)}$对称性的规范下具有一致性。 显示英文摘要

摘要： We investigate the proposition that axion-Yang-Mills systems are characterized by a $3$-form gauge theory in the deep infrared regime. This hypothesis is rigorously examined by initially developing a systematic framework for analyzing $3$-form gauge theory coupled to an axion, specifically focusing on its global properties. The theory consists of a BF term deformed by marginal and irrelevant operators and describes a network of vacua separated by domain walls converging at the junction of an axion string. It encompasses $0$- and $3$-form spontaneously broken global symmetries. Utilizing this framework, in conjunction with effective field theory techniques and 't Hooft anomaly-matching conditions, we argue that the $3$-form gauge theory faithfully captures the infrared physics of the axion-Yang-Mills system. The ultraviolet theory is an $SU(N)$ Yang-Mills theory endowed with a massless Dirac fermion coupled to a complex scalar and is characterized by chiral and genuine $\mathbb{Z}_m^{(1)}$ $1$-form center symmetries, with a mixed anomaly between them. It features two scales: the vev of the complex scalar, $v$, and the strong-coupling scale, $\Lambda$, with $\Lambda \ll v$. Below $v$, the fermion decouples and a $U(1)^{(2)}$ $2$-form winding symmetry emerge, while the $1$-form symmetry is enhanced to $\mathbb Z_N^{(1)}$. As we flow below $\Lambda$, matching the mixed anomaly necessitates introducing a dynamical $3$-form gauge field of $U(1)^{(2)}$, which appears as the incarnation of a long-range tail of the color field. The infrared theory possesses spontaneously broken chiral and emergent $3$-form global symmetries. It passes several checks, among which: it displays the expected restructuring in the hadronic sector upon transition between the vacua, and it is consistent under the gauging of the genuine $\mathbb Z_m^{(1)}\subset \mathbb Z_N^{(1)}$ symmetry.