Global aspects of $3$-form gauge theory: implications for axion-Yang-Mills systems
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arXiv
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| Natura: | Preprint |
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2024
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| author | Anber, Mohamed M. Chan, Samson Y. L. |
| author_facet | Anber, Mohamed M. Chan, Samson Y. L. |
| contents | 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, $Λ$, with $Λ\ll v$. 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 $Λ$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global aspects of $3$-form gauge theory: implications for axion-Yang-Mills systems Anber, Mohamed M. Chan, Samson Y. L. High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology 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, $Λ$, with $Λ\ll v$. 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 $Λ$, 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. |
| title | Global aspects of $3$-form gauge theory: implications for axion-Yang-Mills systems |
| topic | High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.03416 |