Related papers: Harmonic forms on principal bundles

The notion of a gerbe with connection is conveniently reformulated in terms of the simplicial deRham complex. In particular the usual Chern-Weil and Chern-Simons theory is well adapted to this framework and rather easily gives rise to…

A strong from of invariance under a group G is manifested in a family over the classifying space BG. We advocate a differential-geometric avatar of BG when G is a Lie group. Applied to G-equivariant connections on smooth principal or vector…

Using $\mathbb{Z}_3$ symmetry, we present a topological condition for the existence of the $\mathbb{Z}_2$ harmonic 1-forms over Riemannian manifold. As a corollary, if $L$ is an oriented link on $S^3$ with determinant zero, then there…

Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…

A variety is unirational if it is dominated by a rational variety. A variety is rationally connected if two general points can be joined by a rational curve. This paper aims to show that the two notions can cooperate and, building on…

We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…

We study complex Chern-Simons theory on a Seifert manifold $M_3$ by embedding it into string theory. We show that complex Chern-Simons theory on $M_3$ is equivalent to a topologically twisted supersymmetric theory and its partition function…

The abelian Chern-Simons theory is considered on a cylindrical spacetime $\mathbb{R} \times D$, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a…

We prove a criterion for the existence of harmonic metrics on Higgs bundles that are defined on smooth loci of klt varieties. As one application, we resolve the quasi-etale uniformisation problem for minimal varieties of general type to…

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…

The aim of this article is to proof a necessary and sufficient condition for the existence of a Cartan connection on a principal bundle. After collecting the essentially well known facts to fix the terminology, soldering forms and…

A rank $n$ Higgs bundle $(E,\theta)$ is called generically regular nilpotent if $\theta^n=0$ but $\theta^{n-1}\neq 0$. We show that for a generically regular nilpotent Higgs bundle, if it admits a harmonic metric, then its graded Higgs…

Let $f: X \to S$ be flat morphism over an algebraically closed field $k$ with a relative normal crossings divisor $Y\subset X$, $(E, \nabla)$ be a bundle with a connection with log poles along $Y$ and curvature with values in…

While M- and F-theory compactifications describe a much larger class of vacua than perturbative string compactifications, they typically need singularities to generate non-abelian gauge fields and charged matter. The physical explanation…

Every $\mathbb{A}^{1}-$bundle over the complex affine plane punctured at the origin, is trivial in the differentiable category but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of…

We prove that Chern-Weil forms are the only natural differential forms associated to a connection on a principal G-bundle. We use the homotopy theory of simplicial sheaves on smooth manifolds to formulate the theorem and set up the proof.…

In this short review article we sketch some developments which should ultimately lead to the analogy of the Chern-Weil homomorphism for principal bundles in the realm of non-commutative differential geometry. Principal bundles there should…

Large N quasi-fermionic Chern-Simons-matter theories have an approximate higher-spin symmetry that strongly constrains their correlation functions. In particular, the 3-point functions for generic spins are combinations of 3 structures…

Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…

We investigate the quantum consistency of p-form Maxwell-Chern-Simons electrodynamics in 3p+2 spacetime dimensions (for p odd). These are the dimensions where the Chern--Simons term is cubic, i.e., of the form FFA. For the theory to be…