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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.

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Caltech Authors  


Gukov, Sergei -  Sułkowski, Piotr - 

Id.: 55304948

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Tipo de recurso: Article  -  PeerReviewed  - 

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: 04-may-2016


* 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

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