Poincar\'e Gauge Theories for Lineal Garvity

TL;DR

This paper demonstrates that key lineal gravity models, including Liouville gravity and a black-hole-like model, can be formulated as gauge invariant Poincaré theories, with matter couplings and dimensional reductions explored.

Contribution

It introduces a gauge invariant formulation of lineal gravity models as Poincaré gauge theories, including matter couplings and dimensional reduction insights.

Findings

Liouville gravity and a black-hole model are formulated as Poincaré gauge theories.

Explicit matter couplings and solutions are provided.

Models are derived from 2+1-dimensional ISO(2,1) gauge theories.

Abstract

We have shown that two of the most studied models of lineal gravities - Liouville gravity and a ``string-inspired'' model exhibiting the main characteristic features of a black-hole solution - can be formulated as gauge invariant theories of the Poincar\'e group. The gauge invariant couplings to matter (particles, scalar and spinor fields) and explicit solutions for some matter field configurations, are provided. It is shown that both the models, as well as the couplings to matter, can be obtained as suitable dimensional reductions of a 2+1-dimensional ISO(2,1) gauge invariant theory.