Quantum mirror curve of periodic chain geometry

Kimura, Taro; Sugimoto, Yuji

doi:10.1007/jhep04(2019)147

Cited by 4 publications

(3 citation statements)

References 42 publications

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“…Therefore the information about each generalized hypergeometric function r F s is also encoded in a set of integral BPS invariants, or motivic Donaldson-Thomas invariants for the corresponding quiver. Note that brane partition functions in the form of q-hypergeometric functions r+1 φ r , for a special class of strip geometries with all P 1 's of (−1, −1) type, were derived in [24,25], however it seems that the relation between arbitrary strip geometries and all q-hypergeometric functions r φ s has not been discussed before.…”

Section: Introductionmentioning

confidence: 99%

Topological strings, strips and quivers

Panfil

Sułkowski

2019

J. High Energ. Phys.

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We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, also referred to as strip geometries. We show that various quantities that characterize open topological string theory on these manifolds, such as partition functions, Gromov-Witten invariants, or open BPS invariants, can be expressed in terms of characteristics of the moduli space of representations of the corresponding quiver. This has various deep consequences; in particular, expressing open BPS invariants in terms of motivic Donaldson-Thomas invariants, immediately proves integrality of the former ones. Taking advantage of the relation to quivers we also derive explicit expressions for classical open BPS invariants for an arbitrary strip geometry, which lead to a large set of number theoretic integrality statements. Furthermore, for a specific framing, open topological string partition functions for strip geometries take form of generalized q-hypergeometric functions, which leads to a novel representation of these functions in terms of quantum dilogarithms and integral invariants. We also study quantum curves and A-polynomials associated to quivers, various limits thereof, and their specializations relevant for strip geometries. The relation between toric manifolds and quivers can be regarded as a generalization of the knots-quivers correspondence to more general Calabi-Yau geometries.

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Section: Introductionmentioning

confidence: 99%

Topological strings, strips and quivers

Panfil

Sułkowski

2019

J. High Energ. Phys.

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“…In that case, we impose the periodic boundary condition, µ0 = µm+n 5. It might be easier to utilize the operator formalism discussed in[25] than using the formulae about Schur function.…”

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confidence: 99%

Topological vertex/anti-vertex and supergroup gauge theory

Kimura

Sugimoto

2020

J. High Energ. Phys.

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We propose a new vertex formalism, called anti-refined topological vertex (anti-vertex for short), to compute the generalized topological string amplitude, which gives rise to the supergroup gauge theory partition function. We show the one-to-many correspondence between the gauge theory and the Calabi-Yau geometry, which is peculiar to the supergroup theory, and the relation between the ordinary vertex formalism and the vertex/anti-vertex formalism through the analytic continuation.

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“…Consider the open string partition function for a brane attached to the first vertex. It has also been calculated in [27], and takes form…”

Section: Periodic Chain Geometrymentioning

confidence: 99%

Branes, quivers and wave-functions

et al. 2021

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We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating series, and on the other hand as wave-functions in various polarizations. We determine operations on quivers, as well as SL(2,\mathbb{Z})SL(2,ℤ) transformations, which correspond to changing positions of these branes. Our results prove integrality of BPS multiplicities associated to this class of branes, reveal how they transform under changes of polarization, and imply all other properties of brane amplitudes that follow from the relation to quivers.

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Quantum mirror curve of periodic chain geometry

Cited by 4 publications

References 42 publications

Topological strings, strips and quivers

Topological strings, strips and quivers

Topological vertex/anti-vertex and supergroup gauge theory

Branes, quivers and wave-functions

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