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.File | Dimensione | Formato | |
---|---|---|---|
jhep122001024.pdf
Accesso chiuso
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
245.27 kB
Formato
Adobe PDF
|
245.27 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.