Self-consistent theory of polymerized membranes.

We study D-dimensional polymerized membranes embedded in d dimensions using a selfconsistent screening approximation. It is exact for large d to order 1/d, for any d to order ǫ = 4−D and for d = D. For flat physical membranes (D = 2, d = 3) it predicts a roughness exponent ζ = 0.590. For phantom membranes at the crumpling transition the size exponent is ν = 0.732. It yields identical lower critical dimension for the flat phase and crumpling transition Dlc(d) = 2d d+1 (Dlc = √ 2 for codimension 1). For physical membranes with random quenched curvature ζ = 0.775 in the new T = 0 flat phase in good agreement with simulations. PACS: 64.60Fr,05.40,82.65Dp