Related papers: The Lanczos potential and Chern-Simons theory
Using the well-known Chern-Weil formula and its generalization, we systematically construct the Chern-Simons forms and their generalization induced by torsion as well as the Nieh-Yan (N-Y) forms. We also give an argument on the vanishing of…
Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann…
The Chern-Simons perturbation theory gives an invariant $d(M,\rho)$ for a pair of a closed oriented 3-manifold $M$ and a representation $\rho$ of the fundamental group. We generalize $d(M,\rho)$ for compact oriented 3-manifolds with torus…
We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the…
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…
The aim of the current paper is to clarify some aspects of the formalism used for describing the scalar-tensor gravity characterized by four arbitrary local functionals of the scalar field. We recall the objects that are invariant with…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
We reformulate chiral higher-spin Yang-Mills and gravity on $\mathbb{R}^4$ as 'CR-holomorphic' theories of Chern-Simons type; in the most general case, these are Moyal deformed to become non-commutative. They are defined on the space of…
In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a…
We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Noether currents and superpotentials are computed…
In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given…
Among modified gravitational theories, the Tensor-Vector-Scalar (TeVeS) occupies a special place -- it is a covariant theory of gravity that produces the modified Newtonian dynamics (MOND) in the nonrelativistic weak field limit and…
This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension $d=3$. In particular, we find an expression for the superpotential of Chern-Simons gravity. As a by-product the…
When 4-dimensional general relativity is extended by a 3-dimensional gravitational Chern-Simons term an apparent violation of diffeormorphism invariance is extinguished by the dynamical equations of motion for the modified theory. The…
We derive the full N=2 supergravity Lagrangian which contains a symplectic invariant scalar potential in terms of electric and magnetic charges. As shown in reference [1], the appearance of magnetic charges is allowed only if tensor…
Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein-Hilbert gravity. Projective geometry was used long ago by Thomas et. al. to succinctly package equivalent paths encoded by the geodesic…
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M.…
Chern-Simons gauge theories in 2+1 dimensions with multiple gauge fields exhibit novel properties that are analysed here in some detail. A striking feature is the possibility of a non-propagating Chern-Simons field acquiring a massless…
We show that Poincare-invariant topological gravity in even dimensions can be formulated as a transgression field theory in one higher dimension whose gauge connections are associated to linear and nonlinear realizations of the Poincare…
We introduce Weyl n-algebras and show how their factorization homology may be used to define invariants of manifolds. In the appendix we heuristically explain why these invariants must be perturbative Chern-Simons invariants.