# Conserved chiral currents on the boundary of 3D Maxwell theory

## TL;DR

This paper investigates the boundary behavior of 3D Maxwell theory, revealing conserved chiral currents that form a Ka-Moody algebra, with boundary degrees of freedom described by chiral bosons whose properties depend on bulk parameters.

## Contribution

It demonstrates the existence of chiral conserved edge currents satisfying a Ka-Moody algebra in 3D Maxwell theory with boundary, linking boundary degrees of freedom to bulk parameters.

## Key findings

- Boundary currents satisfy a Ka-Moody algebra with central charge inverse to the Maxwell coupling
- Boundary degrees of freedom are two 2D scalar chiral bosons
- Chiralities of boundary bosons depend on bulk Maxwell parameters

## Abstract

In this paper the 3D Maxwell theory with single-sided planar boundary is studied. As a consequence of the existence, on the boundary, of two Ward identities, we find two chiral conserved edge currents satisfying a Ka\c{c}-Moody algebra with central charge equal to the inverse of the Maxwell coupling constant. We show that the boundary degrees of freedom are two 2D scalar chiral bosons whose chiralities depend on the parameters of the bulk Maxwell theory. In particular, the edge chiral bosons may have opposite chiralities, in close analogy with the "spinon" and "holon" currents characterizing the 3D topological insulators.