Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-05-21
Phys.Rev. D66 (2002) 085012
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 22 pages, no figures
Scientific paper
10.1103/PhysRevD.66.085012
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with $n$ windings a non trivial scaling intertwines $n$ and $N$. In the non-commutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group $U(\infty)$. We perform an explicit perturbative calculation of such a loop up to ${\cal O}(g^6)$; rather surprisingly, we find that in the contribution from the crossed graphs (the genuine non-commutative terms) the scaling we mentioned occurs for large $n$ and $N$ in the limit of maximal non-commutativity $\theta=\infty$. We present arguments in favour of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Bassetto Antonio
Nardelli Giuseppe
Torrielli Alessandro
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