Related papers: Conformal Holonomy Equals Ambient Holonomy
We show that given a conformal structure whose holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is always a local metric in the conformal class off a singular set which is Ricci-isotropic and gives…
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using…
Conformal order are isotropic and translationary invariant thermal states of a conformal theory with nonzero expectation value of certain operators. While ubiquitous in bottom-up models of holographic CFTs, conformal order states are…
A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal…
An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's…
We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat…
The aim of this paper is to describe the geometry of conformal structures in Lorentzian signature, which admit a lightlike conformal Killing vector field whose corresponding adjoint tractor acts as complex structure on the standard tractor…
We investigate horizontal conformality of a differential of a map between Riemannian manifolds where the tangent bundles are equipped with Cheeger--Gromoll type metrics. As a corollary, we characterize the differential of a map as a…
We study the holonomy that is associated to a sub-Riemannian structure defined on the kernel of a global contact form. This includes the holonomy of Schouten's horizontal connection as well as of the adapted connection, both canonical…
We prove that any conformally flat submanifold with flat normal bundle in a conformally flat Riemannian manifold is locally holonomic, that is, admits a principal coordinate system. As one of the consequences of this fact, it is shown that…
If the conformal holonomy group $Hol(\mathcal{T})$ of a simply connected space with conformal structure of signature $(2p-1,2q-1)$ is reduced to $\U(p,q)$ then the conformal holonomy is already contained in the special unitary group…
We study in this paper three natural notions of convergence of homogeneous manifolds, namely infinitesimal, local and pointed, and their relationship with a fourth one, which only takes into account the underlying algebraic structure of the…
The aim of this paper and its prequel is to introduce and classify the irreducible holonomy algebras of the projective Tractor connection. This is achieved through the construction of a `projective cone', a Ricci-flat manifold one dimension…
On a conformal manifold, it is well known that parallel sections of the standard tractor bundle with non-vanishing scale are in 1-1 correspondence with solutions of the conformal Einstein equation. In 2 dimensions conformal geometry carries…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
Equivalences between conformal foliations on Euclidean $3$-space, Hermitian structures on Euclidean $4$-space, shear-free ray congruences on Minkowski $4$-space, and holomorphic foliations on complex $4$-space are explained geometrically…
The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit…
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…
Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a…
The analytic structure of solutions to the Klein-Gordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the "hidden conformal symmetry" of a non-extremal…