Related papers: Refined large N duality for knots

Gopakumar-Vafa large N duality is a correspondence between Chern-Simons invariants of a link in a 3-manifold and relative Gromov-Witten invariants of a 6-dimensional symplectic manifold relative to a Lagrangian submanifold. We address the…

We study the spectrum of BPS states in N=4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T^3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in…

We construct three dimensional Chern-Simons-matter theories with gauge groups U(N)xU(N) and SU(N)xSU(N) which have explicit N=6 superconformal symmetry. Using brane constructions we argue that the U(N)xU(N) theory at level k describes the…

Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a…

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become…

We use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces…

Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This…

We consider knot invariants in the context of large $N$ transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicity constructed…

We study the relationship between refined Chern-Simons theory on lens spaces S^3/Z_p and (q,t)-deformed Yang-Mills theory on the sphere S^2. We derive the instanton partition function of (q,t)-deformed U(N) Yang-Mills theory and describe it…

In this work we verify consistency of refined topological string theory from several perspectives. First, we advance the method of computing refined open amplitudes by means of geometric transitions. Based on such computations we show that…

This is an introductory review on the eleven-dimensional description of the BPS bound states of type II superstring theories, and on the role of supermembranes in M-theory. The first part describes classical solutions of 11d supergravity…

We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the $SU(N)_k \times SU(M)_{-k}$ gauge group. At small but fixed $M \ll N$, this system approaches the…

The amplitudes of refined Chern-Simons (CS) theory, colored by antisymmetric (or symmetric) representations, conjecturally generate the Lambda^r- (or S^r-) colored triply graded homology of (n,m) torus knots. This paper is devoted to the…

We consider the large-N limit of \mathcal{N}=6 U(N) \times U(N) superconformal Chern-Simons (ABJM) theory with fixed level k, which is conjectured to be dual to M-theory on AdS4\times (S^7/Z_k) background. We point out that the so-called…

We revisit Dimofte-Gaiotto-Gukov's construction of 3d gauge theories associated to 3-manifolds with a torus boundary. After clarifying their construction from a viewpoint of compactification of a 6d $\mathcal{N}=(2,0)$ theory of $A_1$-type…

Sinha and Vafa \cite {sinha} had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be…

Extending previous work that involved D3-branes ending on a fivebrane with $\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional…

We consider the Gopakumar-Ooguri-Vafa correspondence, relating ${\rm U}(N)$ Chern-Simons theory at large $N$ to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $\mathbb{S}^{\Gamma} =…

We define composite DAHA-superpolynomials of torus knots, depending on pairs of Young diagrams and generalizing the composite HOMFLY-PT polynomials in the theory of the skein of the annulus. We provide various examples. Our superpolynomials…

We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.