Exact vector channel sum rules at finite temperature

The thermal behavior of the spectral function of the electromagnetic current plays an important 
role since it contains the full information on the dilepton/photon production rate, the electrical conductivity, and the modification of the spectral properties of vector mesons at finite temperature. 
In this presentation, we report on the derivation of multiple exact sum rules of this spectral function 
both with zero and non-zero momentum [1,2]. 
We demonstrate that the sum rules are satisfied in the weak coupling regime and discuss how the 
sum rules can be used to determine certain transport coefficients and how they can be applied 
to spectral fits to lattice QCD data. 

[1] P. Gubler and D. Satow, Phys. Rev. D 94, 094042 (2016). 
[2] P. Gubler and D. Satow, Phys. Rev. D 96, 114028 (2017).