In this paper we shall investigate the possibility of solving U(1) theories on the non-commutative (NC) plane for arbitrary values of θ by exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus with a rational parameter θ to the standard U(N) theory in the presence of a 't Hooft flux, whose solution is completely known. Thus, assuming a smooth dependence on θ, we are able to construct a series rational approximants of the original theory, which is finally reached by taking the large-N limit at fixed 't Hooft flux. As we shall see, this procedure hides some subletities since the approach of N to infinity is linked to the shrinking of the commutative two-torus to zero-size. The volume of NC torus instead diverges and it provides a natural cut-off for some intermediate steps of our computation. In this limit, we shall compute both the partition function and the correlator of two Wilson lines. A remarkable fact is that the configurations, providing a finite action in this limit, are in correspondence with the non-commutative solitons (fluxons) found independently by Polychronakos and by Gross and Nekrasov, through a direct computation on the plane.

Towards the Solution of Noncommutative YM(2): Morita Equivalence and Large N-Limit / D. SEMINARA; L. GRIGUOLO; P. VALTANCOLI. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - STAMPA. - 0112:(2001), pp. 0112-1-0112-21. [10.1088/1126-6708/2001/12/024]

Towards the Solution of Noncommutative YM(2): Morita Equivalence and Large N-Limit

SEMINARA, DOMENICO;VALTANCOLI, PAOLO
2001

Abstract

In this paper we shall investigate the possibility of solving U(1) theories on the non-commutative (NC) plane for arbitrary values of θ by exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus with a rational parameter θ to the standard U(N) theory in the presence of a 't Hooft flux, whose solution is completely known. Thus, assuming a smooth dependence on θ, we are able to construct a series rational approximants of the original theory, which is finally reached by taking the large-N limit at fixed 't Hooft flux. As we shall see, this procedure hides some subletities since the approach of N to infinity is linked to the shrinking of the commutative two-torus to zero-size. The volume of NC torus instead diverges and it provides a natural cut-off for some intermediate steps of our computation. In this limit, we shall compute both the partition function and the correlator of two Wilson lines. A remarkable fact is that the configurations, providing a finite action in this limit, are in correspondence with the non-commutative solitons (fluxons) found independently by Polychronakos and by Gross and Nekrasov, through a direct computation on the plane.
2001
0112
0112-1
0112-21
D. SEMINARA; L. GRIGUOLO; P. VALTANCOLI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/12603
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