Coupling to -spin variables located on edges was considered by Ambjørn et al. , who added a Wilson loop term to the action. The matter sector behaves largely as expected when is varied between the crumpled and the elongated gravity phase. However, in the common critical region of both sectors, where a priori one might have expected interesting effects, the critical behaviour seems to agree with that of the pure gravity system.
More recently, Bilke et al.  have reported a non-trivial back-reaction of matter on geometry, when considering coupling to several non-compact -gauge fields. Their study was in part motivated by a continuum analysis of the dynamics of the conformal factor of Antoniadis et al. . Including three fields -fields seems to lead to a total suppression of the branched polymer phase, which is replaced by a new weak-coupling phase with negative susceptibility exponent and a fractal dimension . These are clearly interesting results, but should be treated with some caution because of the small lattice sizes involved ().
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