TL;DR
This paper investigates a specific sector of classical Ashtekar gravity, revealing that Wilson lines behave like 1+1 dimensional spacetimes with propagating massless fields, and explores extensions with matter and supergravity.
Contribution
It introduces the 1+1 sector of Ashtekar gravity and analyzes its properties, including matter and supergravity extensions, highlighting novel behavior of Wilson lines.
Findings
Wilson lines behave like 1+1 dimensional spacetimes
Massless complex fields propagate along Wilson lines
Extensions to matter and supergravity are feasible
Abstract
The rank--1 sector of classical Ashtekar gravity is considered, motivated by the degeneracy of the metric along the Wilson lines in quantum loop states. It is found that the lines behave like 1+1 dimensional spacetimes with a pair of massless complex fields propagating along them. The inclusion of matter and extension to supergravity are also considered.
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