  We calculate and analyse non-local gravitational form factors induced by
quantum matter fields in curved two-dimensional space. The calculations are
performed for scalars, spinors and massive vectors by means of the covariant
heat kernel method up to the second order in the curvature and confirmed using
Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a
generalized "running" form of the Polyakov action for a nonminimal scalar field
and the usual Polyakov action in the conformally invariant cases. In the
infrared (IR) we establish the gravitational decoupling theorem, which can be
seen directly from the form factors or from the physical beta function for
fields of any spin.
