Renormalization of Pinned Elastic Systems: How Does It Work Beyond One Loop?

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their β functions differ to two loops by novel ``anomalous'' terms. At equilibrium we find a roughness ζ0ex0ex=0ex0ex0.20829804ε+0.006858ε² (random bond), ζ0ex0ex=0ex0exε/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find ζ0ex0ex=0ex0exε3(1+0.14331ε), ε0ex0ex=0ex0ex4-d, in violation of the conjecture ζ0ex0ex=0ex0exε/3, solving the discrepancy with simulations. For long range elasticity ζ0ex0ex=0ex0exε3(1+0.39735ε), ε0ex0ex=0ex0ex2-d, much closer to the experimental value ( ≈0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction $1/3$.