The QCD static potential in 2+1 dimensions at weak coupling

Using the effective theory pNRQCD we determine the potential energy of a color singlet quark-antiquark pair with (fixed) distance r in three space-time dimensions at weak coupling (alpha r << 1). The precision of our result reaches O(alpha(3)r(2)), i.e. NNLO in the multipole expansion, and NNLL in a alpha/Delta V expansion, where Delta V similar to alpha In(alpha r). We even include all logarithmic terms up to (NLL)-L-4 order and compare the outcome to existing lattice data.