Novel Edge States in Self-Dual Gravity

TL;DR

This paper explores new edge states in self-dual gravity that emerge despite gauge fixing, potentially impacting black hole information and revealing novel quantum numbers at infinity and horizons.

Contribution

It introduces the concept of edge states in self-dual gravity, characterized by maps from spheres at infinity to SL(2,C), which are not eliminated by gauge fixing.

Findings

Edge states characterized by SL(2,C) maps at infinity.

Edge states lead to mixed states in quantum gravity.

Relevance to black hole information paradox.

Abstract

In contrast to the Einstein-Hilbert action, the action for self-dual gravity contains vierbeins. They are eleminated at the level of observables by an $SL(2,\mathbb{C})$ gauge condition implied by the action. We argue that despite this condition, new "edge" or superselected state vectors corresponding to maps of the spheres $S^2_{\infty}$ at infinity to $SL(2, \mathbb{C})$ arise. They are characterised by new quantum numbers and they lead to mixed states. For black holes, they arise both at the horizon and the spatial infinity and may be relevant for the black hole information paradox. Similar comments can be made about the Einstein-Palatini action which uses vierbeins.