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Knot Invariants from FourDimensional Gauge Theory
 ADV.THEOR.MATH.PHYS
, 2011
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THE HILBERT SCHEME OF A PLANE CURVE SINGULARITY AND THE HOMFLY HOMOLOGY OF ITS LINK
, 2012
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Large N Duality, Mirror Symmetry, and a Qdeformed Apolynomial for Knots
, 2012
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Topological strings and 5d TN partition functions
"... We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5branes, using the refined topological vertex on the dual CalabiYau threefolds. The theories include certain nonLagrangian theories such as the TN theory. The refined topological vertex computation generically ..."
Abstract

Cited by 8 (1 self)
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We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5branes, using the refined topological vertex on the dual CalabiYau threefolds. The theories include certain nonLagrangian theories such as the TN theory. The refined topological vertex computation generically contains contributions from decoupled M2branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T3 theory as well as Sp(1) gauge theories with Nf = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the TN theory. We compute the partition function of the E7 theory via this prescription, and find the E7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to nontoric web diagrams. ar X iv
SU(N) quantum Racah coefficients & nontorus links
, 2013
"... It is wellknown that the SU(2) quantum Racah coefficients or the Wigner 6j symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) ChernSimons field theory. Using isotopy equivalence of SU(N) ChernSimons functional integrals over three balls wit ..."
Abstract

Cited by 5 (2 self)
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It is wellknown that the SU(2) quantum Racah coefficients or the Wigner 6j symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) ChernSimons field theory. Using isotopy equivalence of SU(N) ChernSimons functional integrals over three balls with one or more S2 boundaries with punctures, we obtain identities to be satisfied by the SU(N) quantum Racah coefficients. This enables evaluation of the coefficients for a class of SU(N) representations. Using these coefficients, we can compute the polynomials for some nontorus knots and twocomponent links. These results are useful for verifying conjectures in topological string theory.