Magnetic Helicity, Magnetic Monopoles, and Higgs Winding
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908607443894272 |
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| author | Fukuda, Hajime Hamada, Yuta Kamada, Kohei Mukaida, Kyohei Uchida, Fumio |
| author_facet | Fukuda, Hajime Hamada, Yuta Kamada, Kohei Mukaida, Kyohei Uchida, Fumio |
| contents | Changes in magnetic helicity are often discussed across a variety of fields, from condensed matter physics to early universe cosmology. It is frequently stated that the helicity change is given by the integral of the gauge field strength tensor and its dual over spacetime, $\int F \wedge F$. However, this is incorrect when magnetic monopoles once exist in the spacetime. In this paper, we show the correct formula of the helicity change in such a case for the Maxwell theory with the magnetic monopoles. We also discuss what happens when we embed the Maxwell theory with magnetic monopoles into non-Abelian gauge theories. We show that a similar formula holds for the 't Hooft--Polyakov monopole. In particular, we find the winding numbers and the zeroes of the Higgs field in the non-Abelian gauge theory play a crucial role in the helicity change. The same discussion is also applicable to the electroweak theory, and we discuss the implication of our findings to the baryon number change via the chiral anomaly in the early universe. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_25734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic Helicity, Magnetic Monopoles, and Higgs Winding Fukuda, Hajime Hamada, Yuta Kamada, Kohei Mukaida, Kyohei Uchida, Fumio High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Changes in magnetic helicity are often discussed across a variety of fields, from condensed matter physics to early universe cosmology. It is frequently stated that the helicity change is given by the integral of the gauge field strength tensor and its dual over spacetime, $\int F \wedge F$. However, this is incorrect when magnetic monopoles once exist in the spacetime. In this paper, we show the correct formula of the helicity change in such a case for the Maxwell theory with the magnetic monopoles. We also discuss what happens when we embed the Maxwell theory with magnetic monopoles into non-Abelian gauge theories. We show that a similar formula holds for the 't Hooft--Polyakov monopole. In particular, we find the winding numbers and the zeroes of the Higgs field in the non-Abelian gauge theory play a crucial role in the helicity change. The same discussion is also applicable to the electroweak theory, and we discuss the implication of our findings to the baryon number change via the chiral anomaly in the early universe. |
| title | Magnetic Helicity, Magnetic Monopoles, and Higgs Winding |
| topic | High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.25734 |