2017 Fiscal Year Annual Research Report
Interdisciplinary study of gravity and curvature effect in strongly coupled systems
| Project/Area Number |
17F17763
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| Research Institution | Keio University |
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Principal Investigator |
フラキ アントニノ 慶應義塾大学, 商学部(日吉), 特任准教授 (20444474)
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| Co-Investigator(Kenkyū-buntansha) |
VITAGLIANO VINCENZO 慶應義塾大学, 慶應義塾大学・商学部, 外国人特別研究員
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| Project Period (FY) |
2017-11-10 – 2020-03-31
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| Keywords | Curved space / Symmetry breaking / Quantum fields |
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| Outline of Annual Research Achievements |
During the first five months of the grant, we started our program on the study of general modifications of spontaneous symmetry breaking in curved space. We recently achieved an important result understanding how the breakdown of an internal symmetry gets modified by the competing effects of curvature and topology of spacetime. Our results apply to the Hubbard model on a honeycomb lattice, which makes our result important for applications in graphene. Employing elegant mathematical techniques to calculate the effective action of the theory on a (smoothed) conical space, we were able to find the equations of motion for the fermionic condensate and to solve them numerically, showing how condensation occurs close to the defective region at the apex.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
According to initial plan, during the first five months we tackled the first of the two main lines of the proposed project; we have indeed addressed some of the extremely interesting issues of studying strongly coupled systems in a curved background. Our aim for this project is to understand the way curvature modify the structure of the phase diagram of a self-interacting theory, and the results we have recently achieved are of crucial importance for further developments of the field in very orthogonal directions. Given the exceptionality of our calculation, we have submitted our paper to the most prestigious journal for physics, Physical Review Letters. As already outlined in the proposal, this is the expected first step for a successful completion of the project.
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| Strategy for Future Research Activity |
In the next twelve months we will continue our study on symmetry breaking in curved space. As planned, we have started the study of the validity of Coleman-Mermin-Wagner theorem in curved space. Following the second of the expected main goal of our project, we are going to study possible implications of our results on spontaneous symmetry breaking in curved space, with particular attention to cosmological applications (cosmic strings) and, as emerged in recent discussions, to liquid crystals. Finally, our intention is to explore Casimir effect for interacting systems.
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