A test on analytic continuation of thermal imaginary-time data

Abstract

Some time ago, Cuniberti et al. have proposed a novel method for analytically continuing thermal imaginarytime correlators to real time, which requires no model input and should be applicable with finite-precision data as well. Given that these assertions go against common wisdom, we report on a naive test of the method with an idealized example. We do encounter two problems, which we spell out in detail; this implies that systematic errors are difficult to quantify. On a more positive note, the method is simple to implement and allows for an empirical recipe by which a reasonable qualitative estimate for some transport coefficient may be obtained, if statistical errors of an ultravioletsubtracted imaginary-time measurement can be reduced to roughly below the per mille level.

The shear channel spectral function in hot Yang-Mills theory

“…To this end, an ambitious program was initiated in [13], where the authors tested a numerical recipe for the analytic continuation of Euclidean lattice data to Minkowskian signature. This method in practice amounts to the inversion of an integral relation between the spectral function ρ(ω) and the corresponding imaginary time correlator G(τ ),…”

Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory

“…In the latter case, discussed extensively e.g. in [12], some progress has recently been made in combining lattice measurements of Euclidean correlators with perturbative results for the corresponding spectral functions [13,14]. Despite this, important hydrodynamic parameters such as the shear and bulk viscosities are still outside the realm of accurate first principles calculations.…”

Bulk and scalar spectral densities in weakly and strongly coupled Yang-Mills theory

“…Unfortunately, the nonperturbative evaluation of these functions via lattice QCD is a notoriously challenging problem, and to this end, any input one can gather via weak coupling or gauge/gravity methods is extremely valuable. In particular, perturbation theory may turn out to be of direct use in the analytic continuation of Euclidean lattice data to Minkowskian signature, as recently demon- strated in [26,27,28]. Our hope is indeed that our perturbative spectral functions, derived in [23,24] and discussed in the above sec.…”

“…Due to asymptotic freedom, perturbation theory is expected to provide an accurate description of the UV behavior of various correlators. This makes it a vital ingredient in any attempt to perform an analytic continuation of Euclidean lattice data to Minkowskian signature [26], necessary to obtain nonperturbative first principles predictions for the corresponding transport coefficients. 1 At the same time, the spectral functions (as well as the Euclidean correlation functions that can be determined from them) are also interesting quantities as such.…”