We argue for the existence of a non-trivial fixed point to the 2-d non-linear sigma model corresponding to a non-compact target space of negative curvature. The critical curvature results from a balancing of higher curvature terms against the Einstein term, and consequently occurs near the string-scale. We briefly discuss possible implications for AdS/CFT and AdS/QCD efforts, and also discuss compact hyperbolic manifolds as modulus-free alternatives to Calabi-Yau compactifications.