Conformal symmetry and vortices in graphene

• Thesis title in Czech: Konformní symetrie a víry v grafenu
• Thesis title in English: Conformal symmetry and vortices in graphene
• Key words: gravitační analogie, Diracova ultra-relativistická teorie pole, konformní a Weylova symetrie, Liouvilleova rovnice, netopologická vírová řešení, 2+1 dimenzionální prostoročasy, membrána grafenu
• English key words: gravity analogues, Dirac massless field theory, conformal and Weyl symmetry, Liouville equation, non-topological vortex solutions, 2+1 - dimensional spacetimes, graphene membrane
• Academic year of topic announcement: 2018/2019
• Thesis type: Bachelor's thesis
• Thesis language: angličtina
• Department: Institute of Particle and Nuclear Physics (32-UCJF)
• Supervisor: prof. Alfredo Iorio, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 10.10.2018
• Date of assignment: 10.10.2018
• Confirmed by Study dept. on: 13.05.2019
• Date and time of defence: 25.06.2019 09:00
• Date of electronic submission: 17.05.2019
• Date of submission of printed version: 17.05.2019
• Date of proceeded defence: 25.06.2019
• Opponents: Petr Jizba

Guidelines

The candidate will learn the special features of gravity and Dirac field theory in lower dimensional systems, in particular the (2+1)-dimensional case. Will then move to the application of the above to the idealized case of the law energy excitations of graphene, and will study how conformal symmetry of various kinds are realized there. In this respect, crucial will be the understanding of the role of the Witt and Virasoro algebras, related to the Liouville equation/field theory living on the membrane. One possible outcome of this study is the clarification of the role in graphene, or related spacetimes, of the interesting Chern-Simons vortex solutions of the Liouville equation found by Horvathy-Yera.

References

- Supervisor's notes

- R. Jackiw, Diverse topics in theoretical and mathematical physics, World Scientific Publishing, 1995; R. Jackiw, Weyl symmetry and the Liouville theory, Theoretical and Mathematical Physics, 148 (2006) 941.

- A. Iorio, Weyl-gauge symmetry of graphene, Ann. Phys. 326 (2011) 1334; A. Iorio, L. O'Raifeartaigh, I. Sachs, and C. Wiesendanger, Weyl gauging and conformal invariance, Nucl. Phys. B 495 (1997) 433.

- J. Liouville, Journal de mathématiques pures et appliquées 1re série, 18 (1853) 71.

- P. A. Horvathy, J.-C. Yera, Letters in Mathematical Physics 46 (1998) 111.

- P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory, Springer, 1999.

- C. Nash, S. Sen, Topology and geometry for physicists, Academic Press, 1988; M. Nakahara, Geometry, Topology and Physics (2nd edition), Institute of Physics Publishing, 2003.

- S. Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge University Press, 1998.