The shear channel spectral function in hot Yang-Mills theory

Abstract

We determine a next-to-leading order result for the shear channel thermal spectral function in SU(N ) Yang-Mills theory, working in the limit of vanishing external three-momentum. The result is subsequently applied to the evaluation of the corresponding imaginary time correlator, and its use in the context of sum rules is discussed. Our hope is that the calculation will eventually find use in the nonperturbative determination of the shear viscosity of the theory.

On the infrared behavior of the shear spectral function in hot Yang-Mills theory

“…We notice that the masters I 4' h − I 7' h cancel in the sum of all diagrams, which was to be expected based on their absence in the results of [24].…”

“…This challenge has indeed been addressed first on the level of the Operator Product Expansion (OPE) in [23], and later by considering the full NLO spectral function in [24] (see also the related T = 0 work of [25,26]). While consistent with known sum rules [27,28] as well as the arguments of [29] concerning the UV behavior of various Green's functions, the latter of these calculations delivered somewhat surprising results.…”

“…In the following, we will thus repeat the HTL treatment in the highly analogous shear case (with caveats to be discussed later), hoping to witness similar behavior or at the very least estimate the numerical significance of terms subleading at ω ∼ T , but dominant at ω ∼ gT . In addition, we will also revisit the unresummed calculation of [24], performing a completely independent evaluation of the shear spectral function. These exercises are not only important for the sake of academic interest, but our motivation is also to aid the eventual extraction of the shear viscosity from Euclidean lattice data and to facilitate more accurate comparisons with recent lattice and AdS/CFT calculations [32][33][34][35][36][37][38].…”

“…As the setup of our unresummed calculation is in practice identical to that of [24], we refrain from presenting a lengthy introduction to the technical machinery involved in this part of the work. Instead, we will simply walk the reader through the necessary notations and definitions in section 2.…”

“…As explained in [24], to NLO the shear spectral function obtains contributions from the 1-and 2-loop graphs of figure 1, and can thus be written in the form (…”