Related papers: Harmonic forms on principal bundles
Chern-Simons theory coupled to complex scalars is quantized on the light- front in the local light-cone gauge by constructing the self-consistent hamiltonian theory. It is shown that no inconsistency arises on using two local gauge-fixing…
We give simple homological conditions for a rational homology 3-sphere Y to have infinite order in the rational homology cobordism group, and for a collection of rational homology spheres to be linearly independent. These translate…
The dynamics of five-dimensional Chern-Simons theories is analyzed. These theories are characterized by intricate self couplings which give rise to dynamical features not present in standard theories. As a consequence, Dirac's canonical…
The path integral approach for a 3D Chern-Simons theory is discussed with a focus on the question of metric independence and BRST-exactness in the light of Gribov ambiguity. Copies of the vacuum satisfying the strong boundary conditions and…
We show that conformal Chern-Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor, even when the former is restricted to…
We propose an off-shell construction of three-dimensional N = 3 and N = 4 superconformal Abelian Chern-Simons theories in the projective superspace formalism. We also construct coupling terms among the gauge fields and matter…
We give an example of an orthogonal bundle where the Harder-Narasimhan filtration, with respect to Gieseker semistability, of its underlying vector bundle does not correspond to any parabolic reduction of the orthogonal bundle. A similar…
We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated.…
Nonlinearly realized Abelian global symmetries can be reformulated as local shift symmetries gauged by three-form gauge fields. The anomalous symmetries of the Standard Model (such as Peccei-Quinn or $B+L$) can be dualized to local…
The structure of the five-dimensional Tachyon-Chern-Simons action and its relevance to single-baryon states in the context of the V-QCD models for holographic QCD with backreacting flavor are analyzed. The most general form of the…
We consider a class of "harmonic variations" for nonsingular curves, obtained as asymptotic degenerations along bitangents. On a geometric level, we obtain an attractive relationship between the class and the genus of $C$. The distribution…
In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…
Theorem. Let M be a compact, connected, oriented smooth Riemannian n-manifold with non-empty boundary. Then the cohomology of the complex (Harm*(M),d) of harmonic forms on M is given by the direct sum H^p(Harm*(M),d) = H^p(M;R) +…
A general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of…
Let $C\to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton-Cartan equations for a gauge-invariant Lagrangian density $\Lambda $ on $C$ satisfying a weak condition of regularity, are shown to admit an…
In this article we study the behaviour of semistable principal $G$-bundles over a smooth projective variety $X$ under the extension of structure groups in positive characteristic. We extend some results of Ramanan-Ramanathan…
We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible…
We show that the connection responsible for any abelian or non abelian Aharonov-Bohm effect with $n$ parallel ``magnetic'' flux lines in $\R^3$, lies in a trivial $G$-principal bundle $P\to M$, i.e. $P$ is isomorphic to the product $M\times…
We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle, and are related…
We give an explicitly gauge invariant canonical analysis of linearized quadratic gravity theories in three dimensions for both flat and de-Sitter backgrounds. In flat backgrounds, we also study the effects of gravitational Chern-Simons…