  We will demonstrate that the generalized uncertainty principle exists because
of the derivative expansion in the effective field theories. This is because,
in the framework of the effective field theories, the minimum measurable length
scale has to be integrated away to obtain the low energy effective action. We
will analyze the deformation of a massive free scalar field theory by the
generalized uncertainty principle, and demonstrate that the minimum measurable
length scale corresponds to a second more massive scale in the theory, which
has been integrated away. We will also analyze CFT operators dual to this
deformed scalar field theory, and observe that scaling of the new CFT operators
indicates that they are dual to this more massive scale in the theory. We will
use holographic renormalization to explicitly calculate the renormalized
boundary action with counterterms for this scalar field theory deformed by the
generalized uncertainty principle and show that the generalized uncertainty
principle contributes to the matter conformal anomaly.
