Non-Relativistic Limits of Colored Gravity in Three Dimensions

TL;DR

This paper explores the non-relativistic limits of three-dimensional colored gravity using algebra contractions, revealing how central extensions enable action principles and evade no-go theorems.

Contribution

It introduces a method to obtain non-relativistic colored gravity models via generalized Inönü-Wigner contractions, expanding the understanding of algebraic structures in 3D gravity.

Findings

Non-relativistic limits are achieved through algebra contractions.

Central extensions enable non-degenerate bilinear forms for action principles.

Color-decorated algebras help evade multi-graviton no-go theorems.

Abstract

The three-dimensional non-relativistic isometry algebras, namely Galilei and Newton-Hooke algebras, are known to admit double central extensions, which allows for non-degenerate bilinear forms hence for action principles through Chern-Simons formulation. In three-dimensional colored gravity, the same central extension helps the theory evade the multi-graviton no-go theorems by enlarging the color-decorated isometry algebra. We investigate the non-relativistic limits of three-dimensional colored gravity in terms of generalized \.In\"on\"u-Wigner contractions.