A shear spectral sum rule in a non-conformal gravity dual

Abstract

A sum rule which relates a stress-energy tensor correlator to thermodynamic functions is examined within the context of a simple non-conformal gravity dual. Such a sum rule was previously derived using AdS/CFT for conformal $\mathcal{N}=4$ Supersymmetric Yang-Mills theory, but we show that it does not generalize to the non-conformal theory under consideration. We provide a generalized sum rule and numerically verify its validity. A useful byproduct of the calculation is the computation of the spectral density in a strongly coupled non-conformal theory. Qualitative features of the spectral densities and implications for lattice measurements of transport coefficients are discussed.

Comments: 13 pages, 3 figures. v5: Typos in Eq. (60) fixed. v4: References added, matches published version. v3: Minor typographical corrections. v2: References and some discussion in Appendix A have been added; conclusions unchanged