  We present a unified formulation of a rotationally invariant nonlinear
elasticity for a variety of spontaneously anisotropic phases, and use it to
study thermal fluctuations in nematic elastomers and spontaneously anisotropic
gels. We find that in a thermodynamic limit homogeneous nematic elastomers are
universally incompressible, are characterized by a universal ratio of shear
moduli, and exhibit an anomalous elasticity controlled by a nontrivial low
temperature fixed point perturbative in D=3-epsilon dimensions. In three
dimensions, we make predictions that are asymptotically exact.

Soft Condensed Matter;Disordered Systems and Neural Networks;Materials Science;Statistical Mechanics