Quivers for 3-manifolds: the correspondence, BPS states, and 3d $$ \mathcal{N} $$ = 2 theories

Kucharski, Piotr

doi:10.1007/jhep09(2020)075

Cited by 17 publications

(7 citation statements)

References 45 publications

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“…The knots-quivers correspondence was shown to hold for various knots up to 6 crossings and for some infinite series in [2,3], it was proven for two-bridge knots in [4] and for arborescent knots in [5]. Its relations to topological string theory were further discussed in [6][7][8], and related developments are presented in [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Branes, quivers and wave-functions

Kimura,

Panfil,

Sugimoto

et al. 2020

Preprint

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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, 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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Section: Introductionmentioning

confidence: 99%

Branes, quivers and wave-functions

Kimura,

Panfil,

Sugimoto

et al. 2020

Preprint

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“…Meanwhile, a two-variable knot invariant or an analytic continuation of the colored Jones polynomial with both the Chern-Simons level k and the representation R analytically continued, which is often denoted as F K (x, q) in literature, has been proposed in [3]. A number of aspects of F K (x, q) including calculations and generalizations have been studied, for example, in [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

BPS invariants for Seifert manifolds

Chung

2020

J. High Energ. Phys.

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We calculate the homological blocks for Seifert manifolds from the exact expression for the G = SU (N ) Witten-Reshetikhin-Turaev invariants of Seifert manifolds obtained by Lawrence, Rozansky, and Mariño. For the G = SU (2) case, it is possible to express them in terms of the false theta functions and their derivatives. For G = SU (N ), we calculate them as a series expansion and also discuss some properties of the contributions from the abelian flat connections to the Witten-Reshetikhin-Turaev invariants for general N . We also provide an expected form of the S-matrix for general cases and the structure of the Witten-Reshetikhin-Turaev invariants in terms of the homological blocks.In this paper, we consider the G = SU (N ) WRT invariant on general Seifert manifolds X(P 1 /Q 1 , . . . , P F /Q F ) where P j and Q j are coprime for each j = 1, . . . , F and P j 's are pairwise coprime. We provide a formula that calculates Z a 's from which we can calculate the homological blocks exactly for G = SU (2) and as a q-series expansion for G = SU (N ) from the exact expression given by Lawrence and Rozansky [15] and Mariño [16]. We see that examples calculated in this paper fit into the expected structures of the WRT invariant for Seifert manifolds in terms of homological blocks in section 3.2.3 The reason why only abelian flat connections are taken into account, not all flat connections, is not known yet, though the resurgent analysis provide some explanation on it.The q-series in parenthesis takes a form of q 1 120 Z [[q]]. This agrees with the result of [3] on the Poincaré homology sphere Σ(2, 3, 5). As it is an integer homology sphere, there is one homological block from the trivial flat connection, which is (2.20).

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“…• Last but not least, there is a question about the relation of superintegrability (in the form of Harer-Zagier factorization) to other well-known, and undergoing rapid development, knot-theoretical structures: the knots-quivers correspondence [37][38][39][40] and theory of q-Virasoro localization [41][42][43].…”

Section: Discussionmentioning

confidence: 99%

Harer-Zagier formulas for knot matrix models

Morozov,

Popolitov,

Shakirov

2021

Preprint

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Knot matrix models are defined so that the averages of characters are equal to knot polynomials. From this definition one can extract single trace averages and generation functions for them in the group rank -which generalize the celebrated Harer-Zagier formulas for Hermitian matrix model. We describe the outcome of this program for HOMFLY-PT polynomials of various knots. In particular, we claim that the Harer-Zagier formulas for torus knots factorize nicely, but this does not happen for other knots. This fact is mysteriously parallel to existence of explicit β = 1 eigenvalue model construction for torus knots only, and can be responsible for problems with construction of a similar model for other knots.

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Quivers for 3-manifolds: the correspondence, BPS states, and 3d $$ \mathcal{N} $$ = 2 theories

Cited by 17 publications

References 45 publications

Branes, quivers and wave-functions

Branes, quivers and wave-functions

BPS invariants for Seifert manifolds

Harer-Zagier formulas for knot matrix models

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