On the Holomorphic Gauge Quantization of the Chern-Simons Theory and Laughlin Wave Functions

TL;DR

This paper explores the holomorphic gauge quantization of Chern-Simons theory with noncompact gauge symmetry, proposing a framework that effectively describes quantum Hall states through complex gauge fixing and conjugate fields.

Contribution

It introduces a novel holomorphic gauge quantization approach for Chern-Simons-Matter theories with noncompact gauge groups, linking it to quantum Hall state descriptions.

Findings

Holomorphic gauge fixing is effective for quantizing Chern-Simons theories.

Complex conjugate fields are essential for modeling quantum Hall states.

The framework provides insights into the gauge structure of quantum Hall systems.

Abstract

Chern-Simons-Matter Lagrangian with noncompact gauge symmetry group is considered. The theory is quantized in the holomorphic gauge with a complex gauge fixing condition. The model is discussed, in which the the gauge and matter fields are accompanied by the complex conjugate counterparts. It is argued, that such a theory represents an adequate framework for the description of the quantum Hall states.