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

Abstract

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.

Dressed spectral densities for heavy quark diffusion in holographic plasmas

“…A subtraction similar to the one we perform in this work has been recently advocated in the case of bulk correlators, in [55], in order for the corresponding spectral densities to satisfy appropriate sum rules. Here we are able to justify why this subtraction is physically sensible, in the case of the Langevin process, but we expect that similar arguments can be used for the bulk spectral functions.…”

“…This suggests that we can obtain correlators that are well behaved in the UV, simply by subtracting the zero-temperature spectral densities from the finite temperature one. This method has been already applied in the holographic context for the bulk spectral densities [55]. In the next section we will provide an a priori justification that this is in fact the correct prescription.…”

Next-to-leading order thermal spectral functions in the perturbative domain

“…Noteworthy is also a general discussion concerning the shape of the scalar channel spectral function at small frequencies [25] as well as the mentioned OPE representation of its ultraviolet asymptotics [20]. In addition, sum rules have been analyzed [26], improving on earlier findings [27,28], and further insight has been sought from AdS/CFT inspired models [23,29,30,31]. The corresponding transport coefficients (this yields the bulk viscosity for F F , cf.…”

The confining trailing string

“…The subtracted term is the correlator obtained from the trailing string solution in the vacuum geometry with no black hole. A similar subtraction was adopted in [24] in the case of bulk stress-tensor correlators. The prescription (1.5) can be formally obtained by a change of variables in the heavy-quark path integral, in the limit where the quark mass is much larger than the frequency.…”

“…The subtracted term is the correlator obtained from the trailing string solution in the vacuum geometry with no black hole. A similar subtraction was adopted in [24] in the case of bulk stress-tensor correlators.…”