Scaling properties of the perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory

Abstract

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 $\mathcal{O}(g^6)$; 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.

LaTeX, 22 pages, no figures

References in corpus (4)

• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• Absence of Higher Order Corrections to Noncommutative Chern-Simons Coupling
• Towards the solution of noncommutative $Y{M}_2$: Morita equivalence and large N-limit
• Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory

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