Related papers: On the potential functions for a link diagram
We give a purely topological definition of the perturbative quantum invariants of links and 3-manifolds associated with Chern-Simons field theory. Our definition is as close as possible to one given by Kontsevich. We will also establish…
We extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…
Let $\Delta_{L,\rho_n}(t)$ be the twisted Alexander polynomial with respect to the representation given by the composition of the lift of the holonomy representation of a certain hyperbolic link $L$ and the $n$-dimensional irreducible…
We consider a finite-dimensional oscillatory integral which provides a "finite-dimensional model" for analytically continued $SU(2)$ Chern-Simons theory on closed 3-manifolds that are described by plumbing trees. This model allows an…
Using the thermodynamics formalism, we introduce a notion of intersection for projective Anosov representations, show analyticity results for the intersection and the entropy, and rigidity results for the intersection. We use the…
The CP^N Kazama-Suzuki models with the non-linear chiral algebra SW_infinity[lambda] have been conjectured to be dual to the fully supersymmetric Prokushkin-Vasiliev theory of higher-spin gauge fields coupled to two massive N=2 multiplets…
We extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the $2$-bridge knot orbifolds. As a result we obtain…
A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of \sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior…
Let $M$ be a hyperbolizable $3$-manifold with boundary, and let $\chi_0(M)$ be a component of the $PSL_2\mathbb{C}$-character variety of $M$ that contains the convex co-compact characters. We show that the peripheral map…
We obtain a formula for the Turaev-Viro invariants of a link complement in terms of values of the colored Jones polynomial of the link. As an application we give the first examples for which the volume conjecture of Chen and the third named…
Within the superfield formalism, we calculate the two-point functions and the effective potential for the mass-deformed ${\cal N}=3$ Chern-Simons-matter theory and discuss the related renormalization group issues.
In this paper, we will analyze a three dimensional supersymmetric Chern-Simons theory on a manifold with a boundary. The boundary we will consider in this paper will be defined by $n\cdot x=0$, where $n$ is a light-like vector. It will be…
The Chern-Simons invariants of irreducible U(n)- flat connections on compact hyperbolic 3-manifolds of the form {\Gamma}\H^3 are derived. The explicit formula for the Chern-Simons functional is given in terms of Selberg type zeta functions…
For a recently proposed pure gauge theory in three dimensions, without a Chern-Simons term, we calculate the static interaction potential within the structure of the gauge-invariant variables formalism. The result coincides with that of the…
We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic…
We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an $\mathcal{N}=2$ superconformal field theory to a pure Chern-Simons theory on the…
We characterize $3$-dimensional manifolds represented as connected sums of Lens spaces, copies of $S^2 \times S^1$, and torus bundles over the circle by certain Morse-Bott functions. This adds to our previous result around 2024, classifying…
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…
If $M$ is a finite volume complete hyperbolic 3-manifold with one cusp and no 2-torsion, the geometric component $X_M$ of its $\SL(2,\BC)$-character variety is an affine complex curve, which is smooth at the discrete faithful representation…
We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and…