Geometric aspects of interpolating gauge fixing in Chern-Simons Theory

TL;DR

This paper explores an interpolating gauge fixing method in higher-dimensional abelian Chern-Simons theory, linking it to covariant gauges and analyzing geometric interpretations of linking numbers.

Contribution

It introduces a novel interpolating gauge in higher-dimensional Chern-Simons theory and elucidates its geometric and propagator-related properties.

Findings

Interpolating gauge relates to covariant gauge via anisotropic metric.

Computed propagators for linking number expressions in various gauges.

Clarified geometric interpretations and transitions between them.

Abstract

In this article we investigate an interpolating gauge fixing procedure in $(4l+3)$-dimensional abelian Chern-Simons theory. We show that this interpolating gauge is related to the covariant gauge in a constant anisotropic metric. We compute the corresponding propagators involved in various expressions of the linking number in various gauges. We comment on the geometric interpretations of these expressions, clarifying how to pass from one interpretation to another.