2020 Fiscal Year Research-status Report
Topological Solitons and Non-perturbative Phenomena in Field Theory
| Project/Area Number |
19K14713
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| Research Institution | Keio University |
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Principal Investigator |
チャッタルジー チャンドラセカール 慶應義塾大学, 自然科学研究教育センター(日吉), 訪問研究員 (40837837)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | topological solitons / vortices / cosmic strings / supersymmetry / superconductors / gauge theory |
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| Outline of Annual Research Achievements |
We have discussed what happens when a field that receives an Aharonov-Bohm (AB) phase develops a vacuum expectation value (VEV), using the example of an Alice string in a U(1)×SU(2) gauge theory coupled with complex triplet scalar fields. We have introduced scalar fields belonging to the doublet representation of SU(2), charged or neutral under the U(1) gauge symmetry, that receives an AB phase around the Alice string. When the doublet develops a VEV, the Alice string becomes a global string in the absence of the interaction depending on the relative phase between the doublet and triplet, while in the presence of such an interaction the Alice string is confined by a soliton or domain wall, and therefore the spatial rotation around the string is spontaneously broken.
We have considered the Abelian-Higgs model with two complex scalar fields and arbitrary positive integer charges with the addition to the generalized Josephson term. The theory possesses vortices of both local and global variants. The only finite-energy configurations have been shown to be the local vortices for which a certain combination of vortex numbers and electric charges; called the global vortex number vanishes. The local vortices have rational fractional magnetic flux, as opposed to the global counterparts that can have an arbitrary fractional flux. The global vortices have angular domain walls, which we have found good analytic approximate solutions for. Finally, we have found a full classification of the minimal local vortices as well as a few nonminimal networks of vortices, using numerical methods.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
I have made a progress rather smoothly because I have published two papers in this academic year.
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| Strategy for Future Research Activity |
I will extend our result on Aharonov-Bohm defects of Alice strings to the case of magnetic monopoles.
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| Causes of Carryover |
Because of the COVID-19 pandemic, I could not use the grant for traveling of myself, and honorarium and travel cost for invited speakers, both
of which were supposed to be the main use of the grant.
In this academic year, I plan to use it for article costs, publication fee, honorarium for speakers of online seminars, and so on
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