Duality and Universality for the Chern-Simons bosons

TL;DR

This paper explores phase transitions of Chern-Simons bosons in 2+1 dimensions by mapping to a lattice model, constructing dualities, and analyzing how the Chern-Simons coefficient influences the universality class of the transition.

Contribution

It introduces algebraically exact duality and flux attachment transformations for lattice theories with Chern-Simons terms, linking fractional coefficients to known universality classes.

Findings

Phase transition universality class depends on the Chern-Simons coefficient.

Transformations simplify the model to standard universality classes.

First-order transitions may occur due to irrelevant corrections.

Abstract

By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the Chern-Simons gauge field, we investigate phase transitions of Chern-Simons bosons in the limit of strong coupling. We construct algebraically exact duality and flux attachment transformations of the lattice theories, corresponding to analogous transformations in the continuum limit. These transformations are used to convert the model with arbitrary fractional Chern-Simons coefficient $\alpha$ to a model with $\alpha$ either zero or one. Depending on this final value of $\alpha$, the phase transition in the original model is either in the universality class of the 3D x-y model or a ``fermionic'' universality class, unless the irrelevant corrections of cubic and higher power in momenta render the transition of the first order.