Witten Effect in $3$-Form Description of $θ$-vacua
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908579028533248 |
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| author | Bachmaier, Maximilian Dvali, Gia Valbuena-Bermúdez, Juan Sebastián |
| author_facet | Bachmaier, Maximilian Dvali, Gia Valbuena-Bermúdez, Juan Sebastián |
| contents | The $θ$-vacua of a gauge theory admit an equivalent formulation as vacua of a massless Chern-Simons $3$-form, which originate from the topological susceptibility of the vacuum. This formulation provides a framework in which the physical manifestations of the $θ$-angle, which are quantum in origin, can be captured at the level of effective classical equations of motion. Within this framework, we derive the Witten effect, demonstrating that in the background of a massless $3$-form, the magnetic monopole indeed acquires an electric charge proportional to $θ$. This result, in particular, provides evidence that instantons, even when constrained by the Higgs effect, maintain a non-zero topological susceptibility of the vacuum. In addition to the Witten effect, we numerically demonstrate that a magnetic monopole exhibits polarizability when placed in a constant background electric field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Witten Effect in $3$-Form Description of $θ$-vacua Bachmaier, Maximilian Dvali, Gia Valbuena-Bermúdez, Juan Sebastián High Energy Physics - Theory High Energy Physics - Phenomenology The $θ$-vacua of a gauge theory admit an equivalent formulation as vacua of a massless Chern-Simons $3$-form, which originate from the topological susceptibility of the vacuum. This formulation provides a framework in which the physical manifestations of the $θ$-angle, which are quantum in origin, can be captured at the level of effective classical equations of motion. Within this framework, we derive the Witten effect, demonstrating that in the background of a massless $3$-form, the magnetic monopole indeed acquires an electric charge proportional to $θ$. This result, in particular, provides evidence that instantons, even when constrained by the Higgs effect, maintain a non-zero topological susceptibility of the vacuum. In addition to the Witten effect, we numerically demonstrate that a magnetic monopole exhibits polarizability when placed in a constant background electric field. |
| title | Witten Effect in $3$-Form Description of $θ$-vacua |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2510.05237 |