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We derive three exact sum rules for the spectral function of theelectromagnetic current with zero spatial momentum at finite temperature. Twoof them are derived in this paper for the first time. We explicitly check thatthese sum rules are satisfied in the weak coupling regime and examine which sumrule is sensitive to the transport peak in the spectral function at low energyor the continuum at high energy. Possible applications of the three sum rulesto lattice computations of the spectral function and transport coefficients arealso discussed: We propose an ansatz for the spectral function that can beapplied to all three sum rules and fit it to available lattice data of theEuclidean vector correlator above the critical temperature. As a result, weobtain estimates for both the electrical conductivity $\sigma$ and the secondorder transport coefficient $\tau_J$.

Exact vector channel sum rules at finite temperature and their applications to lattice QCD data analysis