強結合系における重力・曲率効果の分野横断研究

2018 年度 実績報告書

• 研究課題/領域番号: 17F17763
• 研究機関: 慶應義塾大学
• 研究代表者: フラキ アントニノ 慶應義塾大学, 商学部(日吉), 准教授 (20444474)
• 研究分担者: VITAGLIANO VINCENZO 慶應義塾大学, 商学部, 外国人特別研究員
• 研究期間 (年度): 2017-11-10 – 2020-03-31
• キーワード: symmetry breaking / geometry / topology / interacting fields / curved space / topological defects

研究実績の概要

Transitions between broken symmetry and restored symmetry phases are generally triggered by changes in the external conditions, as it happens for example with external magnetic fields, gravity, or temperature. In a series of papers, we have unveiled how geometrical effects enter this picture and challenge the vacuum stability of a theory with four fermion interactions. In particular, we have showed that, for topological defects, the competing action of the locally induced curvature and boundary conditions generated by the non-trivial topology allows configurations where symmetries can be spontaneously broken close to the core of the defect. We further analyzed how a nonzero temperature contributes to temperature-dependent modulation of mass generation in the framework of the “kirigami effect”. Inspired by the effect of geometrical deformations on 2D lattices, we also proposed a novel mechanism to induce a superconducting phase by triggering condensation along cosmic strings. This research is also of paramount importance as a potential path towards inducing a mass-gap in graphene.

現在までの達成度 (区分)

2: おおむね順調に進展している

理由

The project is currently continuing in multiple directions. We are at present working on the analysis of the Casimir effect in the presence of field nonlinearities and its relation with dimensionality, and henceforth with the Mermin-Wagner theorem. In this regard, we also recently started the study of a generalization of the Mermin-Wagner theorem to (thermal) field theories embedded in curved backgrounds.

今後の研究の推進方策

Future works are intended to improve and further extend the application of technics and results of quantum field theory in curved spaces to engineered curved quantum materials. More specifically, we are planning to use a well-known characterization of crystal defects in terms of non-Riemannian quantities (e.g. torsion) and obtain a straightforward inclusion of their effects in the continuum (Lagrangian) description of these systems.

研究成果

• [雑誌論文] Cosmic strings, deformed lattices and spontaneous symmetry breaking (2019)
  • 著者名/発表者名: Antonino Flachi and Vincenzo Vitagliano
  • 雑誌名: J.Phys.Conf.Ser. 巻: 1275 ページ: 0120301-0120305
  • DOI: 10.1088/1742-6596/1275/1/012030
  • オープンアクセス
• [雑誌論文] Black holes, gravitational waves and fundamental physics: a roadmap (2019)
  • 著者名/発表者名: Vincenzo Vitagliano, Leor Barack, Vitor Cardoso, Samaya Nissanke, Diego Blas, Masha Chernyakova, Piotr Chrusciel, Monica Colpi, Valeria Ferrari, Daniele Gaggero, Jonathan Gair, Juan Garcia-Bellido, S. F. Hassan, Lavinia Heisenberg, Martin Hendry, Ik Siong Heng, Carlos Herdeiro, Tanja Hinderer, Assaf Horesh, et al.
  • 雑誌名: Classical and Quantum Gravity 巻: 36 ページ: 1-178
  • DOI: doi.org/10.1088/1361-6382/ab0587
  • 査読あり / 国際共著
• [雑誌論文] Symmetry breaking and lattice kirigami: Finite temperature effects (2019)
  • 著者名/発表者名: Antonino Flachi and Vincenzo Vitagliano
  • 雑誌名: PHYSICAL REVIEW D 巻: 99 ページ: 125010-1-9
  • DOI: doi.org/10.1103/PhysRevD.99.125010
  • 査読あり / オープンアクセス
• [雑誌論文] Symmetry Breaking and Lattice Kirigami (2018)
  • 著者名/発表者名: Antonino Flachi, Vincenzo Vitagliano, Eduardo Castro, Pedro Ribeiro
  • 雑誌名: PHYSICAL REVIEW LETTERS 巻: 121 ページ: 221601-1-5
  • DOI: doi.org/10.1103/PhysRevLett.121.221601
  • 査読あり / オープンアクセス / 国際共著
• [学会発表] Cosmic strings, deformed lattices and spontaneous symmetry breaking (2018)
  • 著者名/発表者名: Vincenzo Vitagliano
  • 学会等名: DICE - Spacetime - Matter - Quantum Mechanics
• [学会発表] Symmetry Breaking and Lattice Kirigami (2018)
  • 著者名/発表者名: Vincenzo Vitagliano
  • 学会等名: Spanish-Portuguese Relativity Meeting - EREP
• [学会発表] Symmetry Breaking and Lattice Kirigami (2018)
  • 著者名/発表者名: Vincenzo Vitagliano
  • 学会等名: Avenues of QFT in Curved Spacetime
• [学会発表] Interacting QFT in topologically deformed manifolds (2018)
  • 著者名/発表者名: Antonino Flachi
  • 学会等名: Marcel Grossmann Meeting (MG15)
• [学会発表] Toying with Symmetry Breaking in Curved Space (2018)
  • 著者名/発表者名: Antonino Flachi
  • 学会等名: Japanese General Relativity and Gravity