Is the $ISO(2,1)$ Gauge Gravity equivalent to the Metric Formulation?

TL;DR

This paper investigates the quantization of the gravitational Chern-Simons coefficient in $ISO(2,1)$ gauge gravity, revealing its inequivalence to the metric formulation and resolving related paradoxes.

Contribution

It demonstrates the inequivalence between $ISO(2,1)$ gauge gravity and the metric formulation, clarifying the conditions under which the Chern-Simons coefficient is quantized.

Findings

Quantization of the Chern-Simons coefficient in both Lorentzian and Euclidean schemes.

Resolution of paradoxes related to gauge gravity quantization.

Evidence that induced spin is not exotic in this context.

Abstract

The quantization of the gravitational Chern-Simons coefficient is investigated in the framework of $ISO(2,1)$ gauge gravity. Some paradoxes involved are cured. The resolution is largely based on the inequivalence of $ISO(2,1)$ gauge gravity and the metric formulation. Both the Lorentzian scheme and the Euclidean scheme lead to the coefficient quantization, which means that the induced spin is not quite exotic in this context.