Related papers: Noncommutative Chern-Simons theory on the quantum …
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…
Noncommutative Maxwell-Chern-Simons theory in 3-dimensions is defined in terms of star product and noncommutative fields. Seiberg-Witten map is employed to write it in terms of ordinary fields. A parent action is introduced and the dual…
Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field
We introduce an anti-symmetric metric into a 3-algebra and call it a symplectic 3-algebra. The N=6, Sp(2N) X U(1) superconformal Chern-Simons-matter theory with SU(4) R-symmetry in three dimensions is constructed by specifying the…
We construct a canonical noncommutative spectral triple for every oriented closed Riemannian manifold, which represents the fundamental class in the twisted K-homology of the manifold. This so-called "projective spectral triple" is Morita…
We give a generalization of Fukaya's Morse homotopy theoretic approach for 2-loop Chern--Simons perturbation theory to 3-valent graphs with arbitrary number of loops at least 2. We construct a sequence of invariants of integral homology…
New methods for computing a variety of gauge theoretic invariants for homology 3-spheres are developed. These invariants include the Chern-Simons invariants, the spectral flow of the odd signature operator, and the rho invariants of…
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…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
The purpose of this article is to apply the concept of the spectral triple, the starting point for the analysis of noncommutative spaces in the sense of A.~Connes, to the case where the algebra $\cA$ contains both bosonic and fermionic…
We consider the Gopakumar-Ooguri-Vafa correspondence, relating ${\rm U}(N)$ Chern-Simons theory at large $N$ to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $\mathbb{S}^{\Gamma} =…
We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this…
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variable as the partition function of a Chern-Simons theory with nontrivial source. The perturbative…
We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semi-Riemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in…
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads…
We discuss Stochastic Quantization of $d$=3 dimensional non-Abelian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the…
Noncommutative Chern-Simons theory can be classically mapped to commutative Chern-Simons theory by the Seiberg-Witten map. We provide evidence that the equivalence persists at the quantum level by computing two and three-point functions of…
The spectral eta function for certain families of Dirac operators on noncommutative $3$-torus is considered and the regularity at zero is proved. By using variational techniques, we show that $\eta_{D}(0)$ is a conformal invariant. By…
We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $\nu=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in…
In this thesis, we studied certain mathematical issues related to the computation of the Chamseddine--Connes spectral action on some fundamental noncommutative spectral triples, such as the noncommutative torus and the quantum 3-sphere…