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# Sum rules for vector channel at finite temperature

Daisuke Satow

The spectral function of the vector current is an important quantity in quark-gluon plasma (QGP) phase, because it contains all the information of the dilepton production rate, electrical conductivity, and the spectrum of vector meson at finite temperature. However, the first principle calculation of this quantity by lattice QCD is still difficult since it is dynamical quantity, not static.In this talk, we derive a few sum-rules which constrain the vector spectral function, by using operator product expansion (OPE) and hydrodynamics, which describes its high/low energy behaviors at finite temperature. We check how these sum rules are satisfied at weak coupling regime by perturbative calculation. We also discuss whether the ansatz for the spectral function used in the lattice QCD calculation satisfies our sum rules.This work is still on-going, so comments and suggestions for improvement are welcomed.