Bosonizations and dualities in 2+1 dimensions
Abstract We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the ℤ 2 f $$ {\mathbb{Z}}_2^f $$ gauging and the flux attachment. The first is primarily a correspondence between topological theories. It amounts to summing over fermionic spin structur...
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2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)107 |
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| author | Andrea Cappelli Riccardo Villa |
| author_facet | Andrea Cappelli Riccardo Villa |
| author_sort | Andrea Cappelli |
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| description | Abstract We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the ℤ 2 f $$ {\mathbb{Z}}_2^f $$ 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 $$ {\mathbb{Z}}_2^f $$ fermion parity emerge from a bosonic theory equipped with a dual ℤ 2 1 $$ {\mathbb{Z}}_2^{(1)} $$ 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 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 $$ {\mathbb{Z}}_2^f $$ gauging to the Dirac-boson and Majorana-boson flux-attachment dualities, we find new relations between bosonic theories. |
| format | Article |
| id | doaj-art-a68d88a7ba3c43f1805e778bcdefcf0c |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-a68d88a7ba3c43f1805e778bcdefcf0c2025-08-20T03:45:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025714610.1007/JHEP07(2025)107Bosonizations and dualities in 2+1 dimensionsAndrea Cappelli0Riccardo Villa1INFN, Sezione di FirenzeINFN, Sezione di FirenzeAbstract We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the ℤ 2 f $$ {\mathbb{Z}}_2^f $$ 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 $$ {\mathbb{Z}}_2^f $$ fermion parity emerge from a bosonic theory equipped with a dual ℤ 2 1 $$ {\mathbb{Z}}_2^{(1)} $$ 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 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 $$ {\mathbb{Z}}_2^f $$ gauging to the Dirac-boson and Majorana-boson flux-attachment dualities, we find new relations between bosonic theories.https://doi.org/10.1007/JHEP07(2025)107Anomalies in Field and String TheoriesScale and Conformal SymmetriesTopological Field TheoriesTopological States of Matter |
| spellingShingle | Andrea Cappelli Riccardo Villa Bosonizations and dualities in 2+1 dimensions Journal of High Energy Physics Anomalies in Field and String Theories Scale and Conformal Symmetries Topological Field Theories Topological States of Matter |
| title | Bosonizations and dualities in 2+1 dimensions |
| title_full | Bosonizations and dualities in 2+1 dimensions |
| title_fullStr | Bosonizations and dualities in 2+1 dimensions |
| title_full_unstemmed | Bosonizations and dualities in 2+1 dimensions |
| title_short | Bosonizations and dualities in 2+1 dimensions |
| title_sort | bosonizations and dualities in 2 1 dimensions |
| topic | Anomalies in Field and String Theories Scale and Conformal Symmetries Topological Field Theories Topological States of Matter |
| url | https://doi.org/10.1007/JHEP07(2025)107 |
| work_keys_str_mv | AT andreacappelli bosonizationsanddualitiesin21dimensions AT riccardovilla bosonizationsanddualitiesin21dimensions |