QCD with adjoint scalars in 2D: properties in the colourless scalar sector Original Research Article

We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. We show that the correlations between Polyakov loops are saturated by two colourless bound states, respectively, even and odd under the Z2 symmetry related to time reversal in the original theory. Their contributions (poles) in correlation functions of local composite operators An, respectively, of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the p=2 operators into polynomials in p=1 operators. In contrast to the naive picture of Debye screening, no sizable signal in any An correlation can be attributed to 1/n times a Debye screening length associated with n elementary fields. These results are quantitatively consistent with the picture of scalar “matter” fields confined within colourless boundstates whose residual “strong” interactions are very weak.