James A. Reid, Charles H. -T. Wang
To the mathematician, the configuration space of the canonical formulation of general relativity is a higher-dimensional analogue of the Teichm\"uller space of conformal structures on a Riemann surface. Using conformal (spin) geometry, we show that the configuration space of conformal connection dynamics is also a higher-dimensional Teichm\"uller space: the moduli space of conformal classes of SU(2) soldering forms. As a corollary, it is noted that the Barbero-Immirzi ambiguity of loop quantum gravity is naturally absent in quantum theories deriving from this formulation of canonical general relativity.
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http://arxiv.org/abs/1102.5560
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