Phases and Duality in Fundamental Kazakov-Migdal Model on the Graph
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913384600961024 |
|---|---|
| author | Matsuura, So Ohta, Kazutoshi |
| author_facet | Matsuura, So Ohta, Kazutoshi |
| contents | We examine the fundamental Kazakov-Migdal (FKM) model on a generic graph, whose partition function is represented by the Ihara zeta function weighted by unitary matrices. The FKM model becomes unstable in the critical strip of the Ihara zeta function. We discover a duality between small and large couplings, associated with the functional equation of the Ihara zeta function for regular graphs. Although the duality is not precise for irregular graphs, we show that the effective action in the large coupling region can be represented by a summation of all possible Wilson loops on the graph similar to that in the small coupling region. We estimate the phase structure of the FKM model both in the small and large coupling regions by comparing it with the Gross-Witten-Wadia (GWW) model. We further validate the theoretical analysis through detailed numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07385 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phases and Duality in Fundamental Kazakov-Migdal Model on the Graph Matsuura, So Ohta, Kazutoshi High Energy Physics - Theory High Energy Physics - Lattice Mathematical Physics We examine the fundamental Kazakov-Migdal (FKM) model on a generic graph, whose partition function is represented by the Ihara zeta function weighted by unitary matrices. The FKM model becomes unstable in the critical strip of the Ihara zeta function. We discover a duality between small and large couplings, associated with the functional equation of the Ihara zeta function for regular graphs. Although the duality is not precise for irregular graphs, we show that the effective action in the large coupling region can be represented by a summation of all possible Wilson loops on the graph similar to that in the small coupling region. We estimate the phase structure of the FKM model both in the small and large coupling regions by comparing it with the Gross-Witten-Wadia (GWW) model. We further validate the theoretical analysis through detailed numerical simulations. |
| title | Phases and Duality in Fundamental Kazakov-Migdal Model on the Graph |
| topic | High Energy Physics - Theory High Energy Physics - Lattice Mathematical Physics |
| url | https://arxiv.org/abs/2403.07385 |