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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2025)107 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |