Related papers: Chern--Simons Perturbation Theory II
We study the set ${\rm vol}\left(M,G\right)$ of volumes of all representations $\rho\co\pi_1M\to G$, where $M$ is a closed oriented $3$-manifold and $G$ is either ${\rm Iso}_+{\Hi}^3$ or ${\rm Iso}_e\t{\rm SL_2(\R)}$. By various methods,…
Chern-Simons Theory with gauge group $SU(N)$ is analyzed from a perturbation theory point of view. The vacuum expectation value of the unknot is computed up to order $g^6$ and it is shown that agreement with the exact result by Witten…
Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory.…
A topological model in three dimensions is proposed. It combines the Chern-Simons action with a BFK-model which was investigated recently by the authors of hep-th/9906146. The finiteness of the model to all orders of perturbation theory is…
We review the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces. This relation has made possible to give an exact solution of topological string theory on these spaces to all orders in…
We couple Chern-Simons gauge theory to 3-dimensional topological gravity with the aim of investigating its quantum topological invariance. We derive the relevant BRST rules and Batalin-Vilkovisky action. Standard BRST transformations of the…
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…
We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical…
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class…
We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the…
We define the notion of spectral network on manifolds of dimension $\le 3$. For a manifold $X$ equipped with a spectral network, we construct equivalences between Chern-Simons invariants of flat ${\mathrm {SL}}(2,{\mathbb C})$-bundles over…
In this note, we revisit the $\Theta$-invariant as defined by R. Bott and the first author. The $\Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
The path integral for the partition function of Chern-Simons gauge theory with a compact gauge group is evaluated on a general Seifert 3-manifold. This extends previous results and relies on abelianisation, a background field method and…
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…
We propose a new, generic mechanism of inflation mediated by a balance between potential forces and a Chern-Simons interaction. Such quasi-topological interactions are ubiquitous in string theory. In the minisuperspace approximation, their…
We apply differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional…
Existence of solutions to the field equations of the gauged Chern-Simons-O(3)-Sigma model on a compact Riemann surface is proved by a topological method. Existence of a minimal deformation constant $\kappa_{*} > 0$ is proved, such that for…
Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the…
We construct a new class of topological surface defects in Chern-Simons theory with non-compact, non-Abelian gauge groups. These defects are characterized by isotropic subalgebras defined by solutions of the modified classical Yang-Baxter…