The Deflation of SU(3)_c at High Temperatures

Abstract

The ideas of "local" and "global" colour-singletness are not well understood within QCD. We use a group theoretical technique to project out the partition function for a system of quarks, antiquarks and gluons to a particular representation of the internal symmetry group $SU(3)_c$: colour-singlet, colour-octet and colour 27-plet at finite temperature. For high temperatures and large size it is shown that colour-singlet is degenerate with colour-octet, colour 27-plet states etc. For the composite system it is shown that $SU(3)_c$ appears to be a good symmetry only at low temperatures and at higher temperatures it gets submerged into a larger group $U(12)_q \otimes U(12)_{\bar{q}}$ (2-flavour). At high enough temperatures this conclusion is model independent. This means that a phase transition from the hadronic matter to the quark-gluon phase implies a transition from the group $SU(3)_c$ to $U(12)_q \otimes U(12)_{\bar q}$. Ideas of extensions beyond the standard model would have to be reviewed in the light of this result.