We derive the sum rule for the spectral function of the stress-energy tensor
in the bulk (uniform dilatation) channel in a general class of strongly coupled
field theories. This class includes theories holographically dual to a theory
of gravity coupled to a single scalar field, representing the operator of the
scale anomaly. In the limit when the operator becomes marginal, the sum rule
coincides with that in QCD. Using the holographic model, we verify explicitly
the cancellation between large and small frequency contributions to the
spectral integral required to satisfy the sum rule in such QCD-like theories.Comment: 16 pages, 2 figure
