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Article overview
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Noncommutative Riemann Surfaces | G. Bertoldi
; J.M. Isidro
; M. Matone
; P. Pasti
; | Date: |
15 Mar 2000 | Subject: | High Energy Physics - Theory; Algebraic Geometry | hep-th math.AG | Abstract: | We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably gauged sl_2(R) algebra. Then a uniquely determined gauge connection provides the central extension which is a 2-cocycle of the 2nd Hochschild cohomology group. Our construction is the double-scaling limit N oinfty, k o-infty of the representation considered in the Narasimhan-Seshadri theorem, which represents the higher-genus analog of ’t Hooft’s clock and shift matrices of QCD. The concept of a noncommutative Riemann surface Sigma_ heta is introduced as a certain C^star-algebra. Finally we investigate the Morita equivalence. | Source: | arXiv, hep-th/0003131 | Services: | Forum | Review | PDF | Favorites |
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