  We investigate hexatic membranes embedded in Euclidean D-dimensional space
using a reparametrization invariant formulation combined with exact
renormalization group (RG) equations. An XY-model coupled to a fluid membrane,
when integrated out, induces long-range interactions between curvatures
described by a Polyakov term in the effective action. We evaluate the
contributions of this term to the running surface tension, bending and Gaussian
rigidities in the approximation of vanishing disclination (vortex) fugacity. We
find a non-Gaussian fixed-point where the membrane is crinkled and has a
non-trivial fractal dimension.
