  We study the correlators of Polyakov loops, and the corresponding gauge
invariant free energy of a static quark-antiquark pair in 2+1 flavor QCD at
finite temperature. Our simulations were carried out on $N_t$ = 6, 8, 10, 12,
16 lattices using Symanzik improved gauge action and a stout improved staggered
action with physical quark masses. The free energies calculated from the
Polyakov loop correlators are extrapolated to the continuum limit. For the free
energies we use a two step renormalization procedure that only uses data at
finite temperature. We also measure correlators with definite Euclidean time
reversal and charge conjugation symmetry to extract two different screening
masses, one in the magnetic, and one in the electric sector, to distinguish two
different correlation lengths in the full Polyakov loop correlator.
