Bosonizations and dualities in 2+1 dimensions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929741339033600 |
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| author | Cappelli, Andrea Villa, Riccardo |
| author_facet | Cappelli, Andrea Villa, Riccardo |
| contents | We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the $Z_2^f$ gauging and the flux attachment. The first is primarily a correspondence between topological theories. It amounts to summing over fermionic spin structures, as is familiar in two-dimensional conformal theories. Its inverse map, fermionization, shows how spin structures and $Z_2^f$ fermion parity emerge from a bosonic theory equipped with a dual $Z_2^{(1)}$ generalized symmetry. The second method,flux attachment, gives spin and statistics to charged particles by coupling them to a Chern-Simons theory, and provides the basis for the Abelian dualities. We illustrate the two bosonizations with explicit results in a solvable semiclassical conformal theory, and show their differences and interplays with particle-vortex dualities. We employ the so-called loop model, which can describe general infrared critical points in 2+1 dimensions in the semiclassical limit. We also combine the two bosonizations to obtain further duality relations. By applying $Z_2^f$ gauging to the Dirac-boson and Majorana-boson flux-attachment dualities, we find new relations between bosonic theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bosonizations and dualities in 2+1 dimensions Cappelli, Andrea Villa, Riccardo High Energy Physics - Theory Strongly Correlated Electrons We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the $Z_2^f$ gauging and the flux attachment. The first is primarily a correspondence between topological theories. It amounts to summing over fermionic spin structures, as is familiar in two-dimensional conformal theories. Its inverse map, fermionization, shows how spin structures and $Z_2^f$ fermion parity emerge from a bosonic theory equipped with a dual $Z_2^{(1)}$ generalized symmetry. The second method,flux attachment, gives spin and statistics to charged particles by coupling them to a Chern-Simons theory, and provides the basis for the Abelian dualities. We illustrate the two bosonizations with explicit results in a solvable semiclassical conformal theory, and show their differences and interplays with particle-vortex dualities. We employ the so-called loop model, which can describe general infrared critical points in 2+1 dimensions in the semiclassical limit. We also combine the two bosonizations to obtain further duality relations. By applying $Z_2^f$ gauging to the Dirac-boson and Majorana-boson flux-attachment dualities, we find new relations between bosonic theories. |
| title | Bosonizations and dualities in 2+1 dimensions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2503.02801 |