Abstract
We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: We propose an ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity σ and the second order transport coefficient τJ .
Highlights
Among the properties of hadronic matter at finite temperature, whose dynamics is described by quantum chromodynamics (QCD), the spectral function of the electromagnetic current plays an important role since it contains the full information on the dilepton/photon production rate [1], the electrical conductivity, and the modification of the spectral properties of vector mesons at finite temperature
The spectral function has naturally been investigated within many approaches, such as perturbative QCD [2], the AdS/CFT correspondence [3], model calculations [4], low-energy effective theory based on hadronic degrees of freedom [5, 6], sum rules [7,8,9,10], and lattice QCD [11,12,13,14,15,16,17,18,19], which have led to a large number of diverse results
One goal of the present paper is to provide such constraints in the form of sum rules, and discuss their applications to lattice QCD analysis
Summary
Among the properties of hadronic matter at finite temperature, whose dynamics is described by quantum chromodynamics (QCD), the spectral function of the electromagnetic current plays an important role since it contains the full information on the dilepton/photon production rate [1], the electrical conductivity, and the modification of the spectral properties of vector mesons at finite temperature. All these quantities have been intensively studied in the context of heavy ion collisions. More detailed analysis is in Ref. [21]
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