We investigate the effect of nonmagnetic disorder on the stability of the
algebraic spin liquid (ASL) by deriving an effective field theory, nonlinear
σ model (NLσM). We find that the anomalous critical exponent
characterizing the criticality of the ASL causes an anomalous gradient in the
NLσM. We show that the sign of the anomalous gradient exponent or the
critical exponent of the ASL determines the stability of the "dirty" ASL. A
positive exponent results in an unstable fixed point separating delocalized and
localized phases, which is consistent with our previous study [Phys. Rev. B
{\bf 70}, 140405 (2004)]. We find power law suppression for the density of
spinon states in contrast to the logarithmic correction in the free Dirac
theory. On the other hand, a negative exponent destabilizes the ASL, causing
the Anderson localization. We discuss the implication of our study in the
pseudogap phase of high Tc​ cuprates