Related papers: Knots, links and branes at large N
We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation)…
We study the framing dependence of the Wilson loop observable of U(N) Chern-Simons gauge theory at large N. Using proposed geometrical large N dual, this leads to a direct computation of certain topological string amplitudes in a closed…
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 revisit the Holographic duality between $SU(N)_\kappa$ Chern-Simons theory and the A-model Topological String Theory. We develop a strategy to systematically compute the large $N$ saddles for correlation functions of Wilson lines in…
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…
Chern-Simons theories, which are topological quantum field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of quantum field theories which can be exactly 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…
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…
In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more…
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…
An elementary introduction to knot theory and its link to quantum field theory is presented with an intention to provide details of some basic calculations in the subject, which are not easily found in texts. Study of Chern-Simons theory…
Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects…
Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of…
The expectation value of a Wilson loop in a Chern--Simons theory is a knot invariant. Its skein relations have been derived in a variety of ways, including variational methods in which small deformations of the loop are made and the changes…
We reconsider topological string realization of SU(N) Chern-Simons theory on S^3. At large N, for every knot K in S^3, we obtain a polynomial A_K(x,p;Q) in two variables x,p depending on the t'Hooft coupling parameter Q=e^{Ng_s}. Its…
A number of results for the level-rank duality of $G(N)_K$ $\leftrightarrow$ $G(K)_N$ Chern-Simons theory are summarized, with emphasis on the applications to knot and link invariants. Explicit examples for $SU(2)_K$ $\leftrightarrow$…
Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants…
A brief summary of the development of perturbative Chern-Simons gauge theory related to the theory of knots and links is presented. Emphasis is made on the progress achieved towards the determination of a general combinatorial expression…
We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct…
The occurrence of the Askey-Wilson (AW) algebra in the $SU(2)$ Chern-Simons (CS) theory and in the Reshetikhin-Turaev (RT) link invariant construction with quantum algebra $U_q(\mathfrak{su}_2)$ is explored. Tangle diagrams with three…