Standard general relativity from Chern-Simons gravity

Il Nuovo Cimento B, 1994

We present a second-order gravity action which consists of ordinary Einstein action augmented by a first-order, vectorlike, Chern-Simons quasitopological term. This theory is ghost-free and propagates a pure spin-2 mode. It is diffeomorphism invariant, although its local Lorentz invariance has been spontaneously broken.

Arxiv preprint hep-th/0512014, 2005

A transgression form is proposed as lagrangian for a gauge field theory. The construction is first carried out for an arbitrary Lie Algebra g and then specialized to some particular cases. We exhibit the action, discuss its symmetries, write down the equations of motion and the boundary conditions that follow from it, and finally compute conserved charges. We also present a method, based on the iterative use of the Extended Cartan Homotopy Formula, which allows one to (i) systematically split the lagrangian in order to appropriately reflect the subspaces structure of the gauge algebra, and (ii) separate the lagrangian in bulk and boundary contributions. Chern-Simons Gravity and Supergravity are then used as examples to illustrate the method. In the end we discuss some further theoretical implications that arise naturally from the mathematical structure being considered.

1999

The dynamical content of local AdS supergravity in five dimensions is discussed. The bosonic sector of the theory contains the vielbein (e a ), the spin connection (ω ab ) and internal SU (N ) and U (1) gauge fields. The fermionic fields are complex Dirac spinors (ψ i ) in a vector representation of SU (N ). All fields together form a connection 1-form in the superalgebra SU (2, 2|N ). For N = 4, the symplectic matrix has maximal rank in a locally AdS background in which the dynamical degrees of freedom can be identified. The resulting efective theory have different numbers of bosonic and fermionic degrees of freedom.

Physics Letters B, 2013

We consider some general consequences of adding pure gravitational Chern-Simons term to manifestly diff-covariant theories of gravity. Extending the result of a previous paper we enlarge the class of metrics for which the inclusion of a gCS term in the action does not affect solutions and corresponding physical quantities. In the case in which such solutions describe black holes (of general horizon topology) we show that the black hole entropy is also unchanged. We arrive at these conclusions by proving three general theorems and studying their consequences. One of the theorems states that the contribution of the gravitational Chern-Simons to the black hole entropy is invariant under local rescaling of the metric. * In string theories compactified to D = 7, they appear in combination when gCS terms are present.

Physics Letters B, 2006

Starting from gravity as a Chern–Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein–Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincaré group enlarged by an Abelian ideal. Although the resulting

Journal of High Energy Physics, 2019

We consider AdS 3 N-extended Chern-Simons supergravity (à la Achucarro-Townsend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion.

International Journal of Modern Physics A, 1998

The usual description of 2 + 1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2 + 1 Einstein gravity. This is done by replacing the Poincaré gauge group symmetry by a q−deformed Poincaré gauge group symmetry, with the former recovered when q → 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2 + 1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to the ordinary ones. Moreover, starting with a properly defined metric tensor, the usual metric theory can be built; the Christoffel symbols and space-time curvature having the usual expressions in terms of the metric tensor, and being represented by c−numbers. In this article, we also couple the theory to particle sources, and find that these sources carry exotic angular momentum. Finally, problems related to the introduction of a cosmological constant are discussed.

Journal of Mathematical Physics, 1991

In this paper de Sitter supergravity theories in 2+1 dimensions with positive cosmological constant as Chern–Simons gauge theories of the algebra OSp(M‖2;C) are constructed. Starting from anti-de Sitter supergravity theories based on OSp(M‖2;R)×OSp(M‖2;R) algebras, a particular Inonu–Wigner contraction is used to construct a large class of super Poincaré supergravity theories with nontrivial internal symmetries. Other models based on algebras SL(M‖N) and the exceptional super Lie algebras are also discussed. The classical consistency of our de Sitter supergravity theories is discussed.

Geometric and Topological Methods for Quantum Field Theory, 2003

These lectures are intended as a broad introduction to Chern Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant action-in the sense of fiber bundles-in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The case of Chern-Simons gravity and its supersymmetric extension for all odd D is presented. No analogous construction is available in even dimensions.