Related papers: Chern-Simons action and the Carrollian Cotton tens…
Chern-Simons invariants of closed oriented Riemannian $3$-manifolds are introduced and studied from the basics. Their first-order variation is the Cotton tensor. The properties of the Cotton tensor: symmetry, conformal covariance, trace-…
The Chern-Simons lagrangian density in the space of metrics of a 3-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is…
A Chern-Simons action written with Christoffel Symbols has a natural gauge symmetry of diffeomorphisms. This Chern-Simons action will induce a Wess-Zumio-Witten model on the boundary of the manifold. If we restrict the diffeomorphisms to…
The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk…
On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives…
A general definition of Chern-Simons actions in non-commutative geometry is proposed and illustrated in several examples. These are based on ``space-times'' which are products of even-dimensional, Riemannian spin manifolds by a discrete…
In this thesis Chern-Simons theories based on Lie algebras with invariant metric are constructed. It is discussed how contractions lead systematically to (higher spin) kinematical algebras of, e.g., Poincar\'e, Galilei and Carroll type and…
The geometric action on a certain orbit of the group of the area-preserving diffeomorphisms is considered, and it is shown, that it coincides with a special reduction of the three-dimensional Chern-Simons theory, under which group and space…
Four-dimensional homogeneous static and rotating black strings in dynamical Chern-Simons modified gravity, with and without torsion, are presented. Each solution is supported by a scalar field that depends linearly on the coordinate that…
A Chern-Simons theory in 11 dimensions, which is a piece of the 11 dimensional supergravity action, is considered as a quantum field theory in its own right. We conjecture that it defines a non-perturbative phase of M theory in which the…
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…
1+3 covariant approach to cosmological perturbation theory often employs the electric part ($E_{ab}$), the magnetic part ($H_{ab}$) of the Weyl tensor or the shear tensor ($\sigma_{ab}$) in a phenomenological description of gravitational…
General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant…
This paper presents conformal invariants for Riemannian manifolds of dimension greater than or equal to four whose vanishing is necessary for a Riemannian manifold to be conformally related to an Einstein space. One of the invariants is a…
Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n+2 dimensions. The manifest classical invariance is achieved using…
The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…
Chern-Simons theories in three dimensions are topological field theories that may have a holographic interpretation for suitable chosen gauge groups and boundary conditions on the fields. Conformal Chern-Simons gravity is a topological…
We consider a complex Hermitian manifold of complex dimensions four with a Hermitian metric and a Chern connection. It is shown that the action that determines the dynamics of the metric is unique, provided that the linearized Einstein…
We study a three-dimensional symmetric Chern-Simons field theory with a general covariance and it turns out that the original Chern-Simons theory is just a gauge fixed action of the symmetric Chern-Simons theory whose constraint algebra…
Recently, the study of three-dimensional spaces is becoming of great interest. In these dimensions the Cotton tensor is prominent as the substitute for the Weyl tensor. It is conformally invariant and its vanishing is equivalent to…