| | |
| | |
Stat |
Members: 3645 Articles: 2'501'711 Articles rated: 2609
19 April 2024 |
|
| | | |
|
Article overview
| |
|
The Concept of a Noncommutative Riemann Surface | G. Bertoldi
; J.M. Isidro
; M. Matone
; P. Pasti
; | Date: |
22 Mar 2000 | Journal: | Phys.Lett. B484 (2000) 323-332 | Subject: | High Energy Physics - Theory; Algebraic Geometry | hep-th math.AG | Abstract: | We consider the compactification M(atrix) theory on a Riemann surface Sigma of genus g>1. A natural generalization of the case of the torus leads to construct a projective unitary representation of pi_1(Sigma), realized on the Hilbert space of square integrable functions on the upper half--plane. A uniquely determined gauge connection, which in turn defines a gauged sl_2(R) algebra, provides the central extension. This has a geometric interpretation as the gauge length of a geodesic triangle, and corresponds to a 2-cocycle of the 2nd Hochschild cohomology group of the Fuchsian group uniformizing Sigma. Our construction can be seen as a suitable double-scaling limit N oinfty, k o-infty of a U(N) representation of pi_1(Sigma), where k is the degree of the associated holomorphic vector bundle, which can be seen as the higher-genus analog of ’t Hooft’s clock and shift matrices of QCD. We compare the above mentioned uniqueness of the connection with the one considered in the differential-geometric approach to the Narasimhan-Seshadri theorem provided by Donaldson. We then use our infinite dimensional representation to construct a C^star-algebra which can be interpreted as a noncommutative Riemann surface Sigma_ heta. Finally, we comment on the extension to higher genus of the concept of Morita equivalence. | Source: | arXiv, hep-th/0003200 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |