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Quantum Curves and D-Modules

Dijkgraaf, R.H. and Hollands, L. and Sulkowski, P. (2008) Quantum Curves and D-Modules. .

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Abstract

In this article we continue our study of chiral fermions on a quantum curve. This system is embedded in string theory as an I-brane configuration, which consists of D4 and D6-branes intersecting along a holomorphic curve in a complex surface, together with a B-field. Mathematically, it is described by a holonomic D-module. Here we focus on spectral curves, which play a prominant role in the theory of (quantum) integrable hierarchies. We show how to associate a quantum state to the I-brane system, and subsequently how to compute quantum invariants. As a first example, this yields an insightful formulation of (double scaled as well as general Hermitian) matrix models. Secondly, our formalism elegantly reconstructs the complete dual Nekrasov-Okounkov partition function from a quantum Seiberg-Witten curve.

Item Type:Article
Institutes:Bureau KNAW
ID Code:3873
Deposited On:27 Aug 2009 12:06
Last Modified:13 Oct 2010 22:35

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