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This article is cited in 4 scientific papers (total in 4 papers)
Balanced Metrics and Noncommutative Kähler Geometry
Sergio Lukić Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855-0849, USA
Abstract:
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions $C^\infty(M)$ on a Kähler manifold $M$. In this setup one interprets $M$ as the phase space itself, equipped with the Poisson brackets inherited from the Kähler 2-form. We compare the geometric
quantization framework with several deformation quantization approaches. We find that the balanced metrics appear naturally as a result of requiring the vacuum energy to be the constant function on the moduli space of semiclassical vacua. In the classical limit these metrics become Kähler–Einstein (when $M$ admits such metrics). Finally, we sketch several applications of this formalism, such as explicit constructions of special Lagrangian submanifolds in compact Calabi–Yau manifolds.
Keywords:
balanced metrics; geometric quantization; Kähler–Einstein.
Received: March 1, 2010; in final form August 2, 2010; Published online August 27, 2010
Citation:
Sergio Lukić, “Balanced Metrics and Noncommutative Kähler Geometry”, SIGMA, 6 (2010), 069, 15 pp.
Linking options:
https://www.mathnet.ru/eng/sigma526 https://www.mathnet.ru/eng/sigma/v6/p69
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