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

Physics – High Energy Physics – High Energy Physics - Theory

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13 pages, 3 figures. v5: Typos in Eq. (60) fixed. v4: References added, matches published version. v3: Minor typographical cor

Scientific paper

10.1103/PhysRevD.82.106005

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.

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