General relativity with a topological phase: an action principle

TL;DR

This paper introduces an action principle unifying general relativity and topological field theories, allowing explicit description of phase transitions and boundary phenomena resembling horizons.

Contribution

It proposes a new action principle with an extra degree of freedom that unifies various formulations of gravity and topological theories, enabling analysis of phase transitions.

Findings

Unified framework for general relativity and topological theories

Explicit description of phase transitions between phases

Boundary phenomena resembling horizons

Abstract

An action principle is described which unifies general relativity and topological field theory. An additional degree of freedom is introduced and depending on the value it takes the theory has solutions that reduce it to 1) general relativity in Palatini form, 2) general relativity in the Ashtekar form, 3) $F\wedge F$ theory for SO(5) and 4) $BF$ theory for SO(5). This theory then makes it possible to describe explicitly the dynamics of phase transition between a topological phase and a gravitational phase where the theory has local degrees of freedom. We also find that a boundary between adymnamical and topological phase resembles an horizon.