Topological phase states of the SU(3) QCD

TL;DR

This paper explores the topological phase states and defects in SU(3) quantum chromodynamics, calculating homotopy groups and identifying six distinct topological phases across different dimensions.

Contribution

It explicitly computes homotopy groups for topological defects in SU(3) QCD and identifies six unique topological phase states in specific dimensions.

Findings

Homotopy groups for SU(3) defects are pi_3=Z, pi_5=Z, pi_6=Z_6.

Six topologically distinct phase states are identified.

Topological invariants are detailed for dimensions 3, 5, and 6.

Abstract

We consider the topologically nontrivial phase states and the corresponding topological defects in the SU(3) d-dimensional quantum chromodynamics (QCD). The homotopy groups for topological classes of such defects are calculated explicitly. We have shown that the three nontrivial groups are pi_3 SU(3)=Z, pi_5 SU(3)=Z, and pi_6 SU(3)=Z_6 if 3 < d < 6. The latter result means that we are dealing exactly with six topologically different phase states. The topological invariants for d=3,5,6 are described in detail.