Related papers: Chern-Simons forms for R-linear connections on Lie…
An analog of Chern-Simons theory is developed in an algebro-geometric setting.
We exhibit the Chern-Simons forms of some characteristic classes in the simplicial de Rham complex.
We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized connections which consist of higher…
Generalized differential forms are employed to construct generalized connections. Lorentzian four-metrics determined by certain of these connections satisfy Einstein's vacuum field equations when the connections are flat. Generalized…
In this paper, we generalize the arithmetic Chern-Simons theory to regular flat separated schemes of finite type over rings of integers of number fields by applying the duality theorems for arithmetic schemes.
We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of these secondary characteristic forms and the relations among…
The aim of this note is to point out that Chern characters can be computed using curvatures o ``super-connections up to homotopy'. We also present an application to the vanishing theorem for Lie algebroids which is at the origin of new…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
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 note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we…
Some properties of Chern-Simons terms are presented and their physical utility is surveyed.
We use some BRS techniques to construct Chern-Simons forms generalizing the Chern character of K_1 groups in the Cuntz-Quillen description of cyclic homology.
We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte's generalization of the Chern-Weil homomorphism.
Simple formulas are given for generating Chern-Simons basic invariant polynomials by repeated exterior differentiation for n-dimensional differentiable manifolds having a general linear connection.
We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections,…
In this paper,we extend the definition of the Chern-Simons type characteristic classes in the continuous case to abelian lattice gauge theory. Then, we show that the exterior differential of a k-th Chern-Simons type characteristic class is…
It has been a long-standing problem how to relate Chern-Simons theory to the quantum groups. In this paper we recover the classical $r$-matrix directly from a 3-dimensional Chern-Simons theory with boundary conditions, thus creating a…
We present a simplification of Neumann's formula for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar…
We investigate metric independent, gauge invariant and closed forms in the generalized YM theory. These forms are polynomial on the corresponding fields strength tensors - curvature forms and are analogous to the Pontryagin-Chern densities…
We show that it is possible to formulate Abelian Chern-Simons theory on a lattice as a topological field theory. We discuss the relationship between gauge invariance of the Chern-Simons lattice action and the topological interpretation of…