Related papers: The Chern-Simons Action in Non-Commutative Geometr…
We consider the Chern-Simons theory with Wilson lines in 3D and in 1D in the BV-BFV formalism of Cattaneo-Mnev-Reshetikhin. In particular, we allow for Wilson lines to end on the boundary of the space-time manifold. In the toy model of 1D…
It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into…
The Chern--Simons term is used in the geometric theory of defects. The equilibrium equations with $\delta$-function source are explicitly solved with respect to the $SO(3)$ connection. This solution describes one straight linear…
We study the Hamiltonian dynamics of a five-dimensional Chern-Simons theory for the gauge algebra $C_5$ of Izaurieta, Rodriguez and Salgado, the so-called S$_H$-expansion of the 5D (anti-)de Sitter algebra (a)ds, based on the cyclic group…
We propose actions for non-linear sigma models on cosets $G/H$ in 2+1 dimensions that include the most general non-linear realizations of Chern-Simons terms. When $G$ is simply connected and $H$ contains $r$ commuting U(1) factors, there…
We construct generalized sets of asymptotic conditions for both three-dimensional Maxwell Chern-Simons gravity and a novel extension that incorporates torsion through a deformation of the Maxwell algebra. These boundary conditions include…
We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on…
We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group $G\ltimes g^*$ on a three-manifold of topology $R \times S$, where $S$ is a surface of genus $g$ with $n+1$ punctures. At each…
In this short note we provide a proof that the Chern-Simons part of the action for N D-branes is invariant under gauge transformations of the RR fields of the type C_p ->C_p + d\Lambda_{p-1}, and rewrite the action in a form that makes this…
In this two-part paper we propose an extension of Connes' notion of even spectral triple to the Lorentzian setting. This extension, which we call a spectral spacetime, is discussed in part II where several natural examples are given which…
We apply ideas of Dijkgraaf and Witten on three-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 classical…
We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, in the presence…
We use differential cohomology to systematically construct a large class of topological actions in physics, including Chern-Simons terms, Wess-Zumino-Novikov-Witten terms, and theta terms (continuous or discrete). We introduce a notion of…
In this paper we explain how to define "lower dimensional'' volumes of any compact Riemannian manifold as the integrals of local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any…
Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge…
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…
A simplified model for a planet's atmosphere as an open two-dimensional Chern-Simons system is presented. The dynamical variables describe an ideal gas by its velocity, mass density, temperature and pressure. Radiation exchange, diffusion…
A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups…
We revisit and clarify some aspects of perturbative renormalization in pure Chern-Simons theory by means of a localization principle associated with an underlying supersymmetry. This perspective allows the otherwise perturbative one-loop…
Non-Abelian gauge theories "live" in a space-time with non-trivial topology that can be characterized by an odd-dimensional Chern-Simons form. In QCD, Chern-Simons form is induced by the chiral anomaly and the presence of topological…