QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector

TL;DR

This paper numerically investigates a 2D SU(3) gauge model with adjoint scalars, revealing properties of colorless boundstates and their correlation functions, consistent with weak residual interactions and confinement.

Contribution

It provides the first detailed numerical analysis of scalar boundstates and correlation functions in a 2D adjoint scalar gauge theory derived from high-temperature QCD.

Findings

Identification of Z_2 even and odd colorless boundstates.

Observation of factorization in correlation function poles.

Detection of two-particle cuts consistent with meanfield estimates.

Abstract

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. In the symmetric phase of its global Z_2 symmetry, two colourless boundstates, even and odd under Z_2, are identified. Their respective contributions (poles) in correlation functions of local composite operators A_n 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. No sizable signal in any A_n 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.