Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-02-19
Mod.Phys.Lett. A7 (1992) 1001-1008
Physics
High Energy Physics
High Energy Physics - Theory
13 pages
Scientific paper
Some time ago, Atiyah showed that there exists a natural identification between the k-instantons of a Yang-Mills theory with gauge group $G$ and the holomorphic maps from $CP_1$ to $\Omega G$. Since then, Nair and Mazur, have associated the $\Theta $ vacua structure in QCD with self-intersecting Riemann surfaces immersed in four dimensions. From here they concluded that these 2D surfaces correspond to the non-perturbative phase of QCD and carry the topological information of the $\Theta$ vacua. In this paper we would like to elaborate on this point by making use of Atiyah's identification. We will argue that an effective description of QCD may be more like a $WZW$ model coupled to the induced metric of an immersion of a 2-D Riemann surface in $R^4$. We make some further comments on the relationship between the coadjoint orbits of the Kac-Moody group on $G$ and instantons with axial symmetry and monopole charge.
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