New Analytical Results on Anisotropic Membranes

We report on recent progress in understanding the tubular phase of self-avoiding anisotropic membranes. After an introduction to the problem, we sketch the renormalization group arguments and symmetry considerations that lead us to the most plausible fixed point structure of the model. We then employ an epsilon-expansion about the upper critical dimension to extrapolate to the physical interesting 3-dimensional case. The results are $\nu=0.62$ for the Flory exponent and $\zeta=0.80$ for the roughness exponent. Finally we comment on the importance that numerical tests may have to test these predictions.