Induced Spin from the $ISO(2,1)$ Gauge Theory with the Gravitational Chern-Simons Term

TL;DR

This paper explores how the gravitational Chern-Simons term in a (2+1)-dimensional $ISO(2,1)$ gauge theory induces spin effects in solutions involving massive particles, revealing globally nontrivial structures.

Contribution

It provides an exact solution showing the gravitational Chern-Simons term induces spin in (2+1)D gravity with nontrivial global features.

Findings

Exact solutions demonstrate CST induces spin effects.

Solutions exhibit conical and helical structures.

Global nontrivialness persists despite local triviality.

Abstract

In the context of $ISO(2,1)$ gauge theory, we consider $(2+1)$-dimensional gravity with the gravitational Chern-Simons term (CST). This formulation allows the `exact' solution for the system coupled to a massive point particle (which is not the case in the conventional Chern-Simons gravity). The solution exhibits locally trivial structure even with the CST, although still shows globally nontrivialness such as the conical space and the helical time structure. Since the solution is exact, we can say the CST induces spin even for noncritical case of $\s+\al m\ne 0$.