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

TL;DR

This paper derives three exact sum rules for the electromagnetic spectral function at finite temperature, including two novel sum rules, and demonstrates their application in analyzing lattice QCD data to estimate transport coefficients like electrical conductivity.

Contribution

It introduces two new exact sum rules for the spectral function at finite temperature and applies them to lattice QCD data to extract transport coefficients.

Findings

Sum rules are satisfied in the weak coupling regime.

A spectral function ansatz fits lattice data and estimates conductivity.

Transport coefficients like  and  are estimated from lattice data.

Abstract

We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. 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 $\sigma$ and the second order transport coefficient $\tau_J$.