Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants

Mariño, Marcos

doi:10.1007/s00220-004-1194-4

Cited by 259 publications

(520 citation statements)

References 43 publications

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“…Different choices of parametrization of this point lead to different types of D-branes, as we will discuss in more detail. According to the conjecture of [37,8], higher open string amplitudes for toric branes can be obtained by applying the topological recursion of [19] to the spectral curve (3.10).…”

Section: Symplectic Transformations In the Resolved Conifoldmentioning

confidence: 99%

“…Finally, the techniques developed in this paper to analyze the matrix model for torus knots will probably be very useful in order to understand the large N limit of the more general matrix models for Seifert spheres introduced in [37]. Such a large N limit would give a way to derive the dual string geometries to Chern-Simons theory in more general rational homology spheres -a dual which has remained elusive so far.…”

Section: Conclusion and Prospects For Future Workmentioning

confidence: 99%

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Torus Knots and Mirror Symmetry

Brini

Mariño

Eynard

2012

Ann. Henri Poincaré

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142

214

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We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.arXiv:1105

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Section: Symplectic Transformations In the Resolved Conifoldmentioning

confidence: 99%

Section: Conclusion and Prospects For Future Workmentioning

confidence: 99%

Torus Knots and Mirror Symmetry

Brini

Mariño

Eynard

2012

Ann. Henri Poincaré

Self Cite

142

214

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show abstract

“…(3.11) By using the strategy of [27,28] in the large k limit, keeping N fixed, (3.11) reduces to (up to an overall factor)…”

Section: Su (N ) K With N F Fundamentals and Anti-fundamentalsmentioning

confidence: 99%

$ \mathcal{Z} $ extremization in chiral-like Chern-Simons theories

Amariti

Siani

2012

J. High Energ. Phys.

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Abstract:We study the localized free energy on S 3 of three-dimensional N = 2 Chern-Simons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard saddle point approximation for large N . We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.arXiv:1109.4152v1 [hep-th]

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“…In [7,8] it was shown that CS theory on S 3 /Z p has a matrix model description. In [8] it was also shown that Holomorphic Chern-Simons (HCS) theory reduced to P 1 's inside the mirror (call it X) to T * (S 3 /Z p ) has a matrix model description.…”

Section: Introductionmentioning

confidence: 99%