Related papers: On the Structure of Wave Functions in Complex Cher…
Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…
We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr's holomorphic almost periodic functions on tube domains or algebras of all…
We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory,…
The perturbative Chern-Simons theory for knots in Euclidean space is a linear combination of integrals on configuration spaces. This has been successively studied by Bott and Taubes, Altschuler and Freidel, and Yang. We study it again in…
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
We explain how to construct certain potential functions for the hyperbolic structures of a knot complement, which are closely related to the analytic functions on the deformation space of hyperbolic structures.
Kohn-Sham (KS) formalism of Density Functional Theory is modified to include the systems with strong non-dynamic electron correlation. Unlike in extended KS and broken symmetry unrestricted KS formalisms, cases of both singlet-triplet and…
In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define…
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…
In this paper we analyze the quantum homological invariants (the Poincar\'e polynomials of the $\mathfrak{sl}_N$ link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the…
We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order…
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
We discuss a matrix of periodic holomorphic functions in the upper and lower half-plane which can be obtained from a factorization of an Andersen-Kashaev state integral of a knot complement with remarkable analytic and asymptotic properties…
In the previous paper arXiv:1711.07122, we show that a holomorphic zero-mode wave function in abelian Chern-Simons theory on the torus can be considered as a quantum version of a modular form of weight 2. Motivated by this result, in this…
Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil…
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…
We decompose sphere partition functions and indices of three-dimensional N=2 gauge theories into a sum of products involving a universal set of "holomorphic blocks". The blocks count BPS states and are in one-to-one correspondence with the…
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)…
There is a large mathematical literature on classical mechanics and field theory, especially on the relationship to symplectic geometry. One might think that the classical Chern-Simons theory, which is topological and so has vanishing…