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

Bassetto, A, Nardelli, G and Torrielli, A (2002) Scaling properties of the perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory Phys.Rev. D, 66. 085012 - ?.

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

Item Type: Article
Additional Information: Copyright 2002 The American Physical Society
Related URLs:
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 27 Jan 2012 12:29
Last Modified: 23 Sep 2013 18:57
URI: http://epubs.surrey.ac.uk/id/eprint/72395

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