Bosonizations and dualities in 2+1 dimensions
Andrea Cappelli, Riccardo Villa · Journal of High Energy Physics · 2025
A bstract We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the $$ {\mathbb{Z}}_2^f $$ 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 $$ {\mathbb{Z}}_2^f $$ ℤ 2 f fermion parity emerge from a bosonic theory equipped with a dual $$ {\mathbb{Z}}_2^{(1)} $$ 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 $$ {\mathbb{Z}}_2^f $$ ℤ 2 f gauging to the Dirac-boson and Majorana-boson flux-attachment dualities, we find new relations between bosonic theories.