Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory |
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| Institution: | 1. Medical Biochemistry Department, Faculty of Medicine, Zagazig University, Zagazig, Egypt;2. Paediatrics Department, Faculty of Medicine, Zagazig University, Zagazig, Egypt;1. Departamento de Genética, Hospital General de México, Facultad de Medicina, Universidad Nacional Autónoma de México, D.F. México, Mexico;2. Departamento de Oftalmología, Hospital General de México, D.F. México, Mexico;3. Departamento de Genética, Centro Médico Ecatepec, ISSEMYM. Edo. México, Mexico;1. Department of Obstetrics and Gynecology, Mackay Memorial Hospital, Taipei, Taiwan;2. Department of Medical Research, Mackay Memorial Hospital, Taipei, Taiwan;3. Department of Biotechnology, Asia University, Taichung, Taiwan;4. School of Chinese Medicine, College of Chinese Medicine, China Medical University, Taichung, Taiwan;5. Institute of Clinical and Community Health Nursing, National Yang-Ming University, Taipei, Taiwan;6. Department of Obstetrics and Gynecology, School of Medicine, National Yang-Ming University, Taipei, Taiwan;7. Department of Obstetrics and Gynecology, Hsinchu Mackay Memorial Hospital, Hsinchu, Taiwan;8. Gene Biodesign Co. Ltd, Taipei, Taiwan;9. Department of Obstetrics and Gynecology, China Medical University Hospital, Taichung, Taiwan;10. Department of Bioengineering, Tatung University, Taipei, Taiwan;1. Department of Geriatrics, Qilu Hospital of Shandong University, Jinan, People''s Republic of China;2. Department of Pharmacy, Qilu Hospital of Shandong University, Jinan, People''s Republic of China |
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| Abstract: | We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang–Mills theory. The trajectories of these “hedgehog loops” are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang–Mills theory that the density of hedgehog structures in the thermal Wilson–Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark–gluon plasma in high-energy heavy-ion collisions. |
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