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Caltech Authors
Descripción: Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly in a suitable semi-classical limit, as ħ → 0, and becomes non-commutative or “quantum” away from this limit. For a classical curve defined by the zero locus of a polynomial A(x, y), we provide a construction of its non-commutative counterpart Â(^x, ^y) using the technique of the topological recursion. This leads to a powerful and systematic algorithm for computing  that, surprisingly, turns out to be much simpler than any of the existent methods. In particular, as a bonus feature of our approach comes a curious observation that, for all curves that come from knots or topological strings, their non-commutative counterparts can be determined just from the first few steps of the topological recursion. We also propose a Ktheory criterion for a curve to be “quantizable,” and then apply our construction to many examples that come from applications to knots, strings, instantons, and random matrices.
Autor(es): Gukov, Sergei - Sułkowski, Piotr -
Id.: 55304948
Versión: 1.0
Estado: Final
Tipo: application/pdf -
Tipo de recurso:
Article
- PeerReviewed
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Tipo de Interactividad: Expositivo
Nivel de Interactividad: muy bajo
Audiencia:
Estudiante
- Profesor
- Autor
-
Estructura: Atomic
Coste: no
Copyright: sí
Formatos: application/pdf -
Requerimientos técnicos: Browser: Any -
Relación:
[References] http://resolver.caltech.edu/CaltechAUTHORS:20120511-113608838
[References] http://authors.library.caltech.edu/31436/
Fecha de contribución: 07-mar-2013
Contacto:
Localización:
* Gukov, Sergei and Sułkowski, Piotr (2012) A-polynomial, B-model, and quantization. Journal of High Energy Physics, 2012 (2). Art. No. 070. ISSN 1126-6708 http://resolver.caltech.edu/CaltechAUTHORS:20120511-113608838
