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The rank--1 sector of classical Ashtekar gravity is considered, motivated bythe degeneracy of the metric along the Wilson lines in quantum loop states. Itis found that the lines behave like 1+1 dimensional spacetimes with a pair ofmassless complex fields propagating along them. The inclusion of matter andextension to supergravity are also considered.Comment: 9 pages, plain Latex, no figure

1 + 1 sector of 3 + 1 gravity