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This function is computed by lattice Monte Carlo in SU(2) pure gauge theory at lattice couplings $\\beta=2.2$ and $\\beta=2.5$ in both Coulomb and Landau gauges. The Coulomb gauge correlator is well behaved, and is dominated at large T by a state whose energy grows linearly as $\\sigma R$, with $\\sigma$ the known asymptotic string tension. The connected correlator in Landau gauge behaves differently. 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