# Resonant algebras in Chern-Simons model of topological insulators

## TL;DR

This paper investigates the use of resonant algebras within Chern-Simons theory to model topological insulators, offering new algebraic frameworks and Lagrangians for their description.

## Contribution

It introduces a novel application of Maxwell and resonant algebras in formulating Chern-Simons models for topological insulators, including multiple Lagrangians with adjustable parameters.

## Key findings

- Six distinct Chern-Simons Lagrangians constructed
- Inclusion of relativistic Wen-Zee and related terms
- Potential applications in generalized (2+1) gravity models

## Abstract

This paper explores the possibility of using Maxwell algebra and its generalizations called resonant algebras for the unified description of topological insulators. We offer the natural action construction, which includes the relativistic Wen-Zee and other terms, with adjustable coupling constants. By gauging all available resonant algebras formed by Lorentz, translational and Maxwell generators $\{J_a, P_a, Z_a\}$ we present six Chern-Simons Lagrangians with various terms content accounting for different aspects of the topological insulators. Additionally, we provide complementary actions for another invariant metric form, which might turn out useful in some generalized (2+1) gravity models.