2017 Fiscal Year Annual Research Report
Topological Solitons and Non-perturbative Effects in Field Theory
| Project/Area Number |
16F16322
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| Research Institution | Keio University |
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Principal Investigator |
新田 宗土 慶應義塾大学, 商学部(日吉), 教授 (60433736)
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| Co-Investigator(Kenkyū-buntansha) |
CHATTERJEE CHANDRASEKHAR 慶應義塾大学, 自然科学研究教育センター, 外国人特別研究員
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| Project Period (FY) |
2016-11-07 – 2019-03-31
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| Keywords | Topological solitons / Non-Abelian strings / Cosmic strings / Supersymmetry / Beyond standard model |
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| Outline of Annual Research Achievements |
1)Recently we found a BPS Alice string and it is a half BPS state preserving a half of supercharges when embedded into a supersymmetric gauge theory. We study zero modes of a BPS Alice string. After presenting U(1) and translational zero modes, we have constructed the effective action of these modes. In contrast to previous analysis of the conventional Alice string for which only large distance behaviors are known, we have performed calculation exactly in the full space thanks to BPS properties.
2)We have studied topological defects in the Georgi-Machacek model. We have found a possibility of topologically stable non-Abelian domain walls and non-Abelian flux tubes in this model. In the limit of the vanishing U(1)Y gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to S2 Nambu-Goldstone (NG) modes localized around the vortex corresponding to non-Abelian fluxes. By taking into account the U(1)Y gauge coupling, the custodial symmetry is explicitly broken and all non-Abelian vortices fall into a topologically stable Z-string. This is in contrast to the Standard Model(SM) in which Z-strings are non-topological and are unstable in the realistic parameter region. We have discussed the existence of domain wall solutions bounded by flux tubes, where their S2 NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a flux tube loop, and would be cosmologically safe. Gravitational waves produced from domain walls could be detected by future experiments.
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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
In addition to carrying out the proposed researches, we have been able to start a new project which was unexpected in the previous fiscal year. Namely, we have already written a reprint paper“Topological Defects in the Georgi-Machacek Model,” arXiv:1801.10469 [hep-ph], which is a 20 page papee. We have made a new theoretical discovery by showing existence of stable topological Z-string in the model known as Georgi-Machacek Model which is one of the models that may help us to understand beyond standard model scenario after the discovery of Higgs boson. We are studying other aspect of our discovery and hopefully we may get some more new results soon.
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| Strategy for Future Research Activity |
1)We have found a model of‘Alice string’which can saturate the BPS bound in U(1)×SO(3) gauge theory with charged complex scalar fields belonging to the vector representation. Our goal is to understand‘Cheshire charge’in multi vortex system by computing zero modes and study braiding of vortices. We want to generalize the system for SU(N) and SO(N) gauge theories and compute the effective action for the zero modes. Beside these mathematical developments I am studying the system numerically. We are developing a numerical code which can be used to study the properties of the system, interactions with other fields, existence of other defects such as domain walls, monopole and their decay in this system.
2)The Standard Model (SM) had been established as a reasonable low-energy effective description of the elementary particle physics. However, SM has theoretical problems, including hierarchy problem, and it does not explain various things such as the neutrino mass, baryon asymmetry, dark matter, etc. These shortcomings of SM might originate from its Higgs sector. This thought motivates us to study extended models of the Higgs sector, such as, Georgi-Machacek (GM) model. We recently have discussed topological defects in the GM model in a hierarchical symmetry breaking. In future I would like to study this model analytically and numerically for the better understanding of the hierarchical symmetry breaking, vacuum decay of domain walls and I would like to work on the effective action of vortex domain wall composite in terms of NG modes with unbroken custodial symmetry.
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