Related papers: Orientifolds and the Refined Topological String
We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle…
We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string…
We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes. We derive the refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link invariant of…
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold…
The refined Chern-Simons theory is a one-parameter deformation of the ordinary Chern-Simons theory on Seifert manifolds. It is defined via an index of the theory on N M5 branes, where the corresponding one-parameter deformation is a natural…
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 study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the…
Large N duality conjecture between U(N) Chern-Simons gauge theory on $S^3$ and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the…
Sinha and Vafa 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 rewritten in…
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…
We present the partition function of the refined Chern-Simons theory on $S^3$ with arbitrary A,B,C,D gauge algebra in terms of multiple sine functions. For B and C cases this representation is novel. It allows us to conjecture duality to…
Aganagic and Shakirov propose a refinement of the SU(N) Chern-Simons theory for links in three manifolds with S^1-symmetry, such as torus knots in S^3, based on deformation of the S and T matrices, originally found by Kirillov and…
We make a precision test of a recently proposed conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold. First, we develop a systematic procedure to extract string amplitudes from vacuum…
We study the large N limit of SO(N) and Sp(N) Chern-Simons gauge theory on S^3 and identify its closed string dual as topological strings on an orientifold of the small resolution of the conifold. Applications to large N dualities for N=1…
The partition function of refined Chern-Simons theory on 3d sphere for the exceptional $E_n$ gauge algebras is presented in terms of multiple sine functions. Gopakumar-Vafa (BPS) approximation is calculated and presented in the form of some…
We present the partition function of Chern-Simons theory with the exceptional gauge group on three-sphere in the form of a partition function of the refined closed topological string with relation $2\tau=g_s(1-b) $ between single K\"ahler…
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…
Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in…
We consider a string dual of a partially topological $U(N)$ Chern-Simons-matter (PTCSM) theory recently introduced by Aganagic, Costello, McNamara and Vafa. In this theory, fundamental matter fields are coupled to the Chern-Simons theory in…
We study the relation between the partition function of refined SU(N) and SO(2N) Chern-Simons on the 3-sphere and the universal Chern-Simons partition function in the sense of Mkrtchyan and Veselov. We find a four-parameter generalization…