Bulk spectral function sum rule in QCD-like theories with a holographic dual

Understand

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.