Related papers: The dilogarithm and abelian Chern-Simons
We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the…
In this paper, we show how to discretize the abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary 2D closed orientable manifolds. We find that, as long as a…
In this paper we introduce the Cheeger-Simons cohomology of a global quotient orbifold. We prove that the Cheeger-Simons cohomology of the orbifold is isomorphic to its Beilinson-Deligne cohomology. Furthermore we construct a string…
We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold $M$ with complex gauge group $G$. We focus on the case $G=SL(N,\mathbb{C})$ and with $M$ a knot complement. The main result presented in this note is the…
Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also…
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…
Chern--Simons type Lagrangians in $d=3$ dimensions are analyzed from the point of view of their covariance and globality. We use the transgression formula to find out a new fully covariant and global Lagrangian for Chern--Simons gravity:…
We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the…
In this article we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson-fermion correspondence, the analytic torsion, the Chern-Simons and $\eta$ invariants, as well as the generation function…
In this note we present a brief overview of connections between Chern-Simons theory and topological strings. A prominent role in this link has been played by large N dualities and holography. We demystify this by explaining why the Kahler…
We define a structure of an algebra on the Lagrangian Floer cohomology of a Lagrangian submanifold over the quantum cohomology of the ambient symplectic manifold. The structure is analogous to the one defined by Biran-Cornea, but is…
In the present paper we study the structure of C*-$algebras generated by a certain *-algebra A and a partial isometry inducing an endomorphism of A.
We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
We use the Chern-Simons action for a SO(3)-connection for the description of point disclinations in the geometric theory of defects. The most general spherically symmetric SO(3)-connection with zero curvature is found. The corresponding…
We study a three-dimensional symmetric Chern-Simons field theory with a general covariance and it turns out that the original Chern-Simons theory is just a gauge fixed action of the symmetric Chern-Simons theory whose constraint algebra…
This is a survey of work in which the author was involved in recent years. We consider C*-algebras constructed from representations of one or several algebraic endomorphisms of a compact abelian group - or, dually, of a discrete abelian…
We study dipole Chern-Simons theory with and without a cosmological constant in $2+1$ dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which…
Various asymmetric orbifold models based on chiral shifts and chiral reflections are investigated. Special attention is devoted to the consistency of the models with two fundamental principles for asymmetric orbifolds : modular invariance…
In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general…