Scalar and tensorial topological matter coupled to (2 + 1)-dimensional gravity: I. Classical theory and global charges (original) (raw)

From Lorentz-Chern-Simons to Massive Gravity in 2+1 dimensions

Journal of High Energy Physics, 2015

We propose a generalization of Chiral Gravity, which follows from considering a Chern-Simons action for the spin connection with anti-symmetric contorsion. The theory corresponds to Topologically Massive Gravity at the chiral point non-minimally coupled to an additional scalar mode that gathers the torsion degree of freedom. In this setup, the effective cosmological constant (the inverse of the curvature radius of maximally symmetric solutions) is either negative or zero, and it enters as an integration constant associated to the value of the contorsion at infinity. We explain how this is not in conflict with the Zamolodchikov's c-theorem holding in the dual boundary theory. In fact, we conjecture that the theory formulated about three-dimensional Anti-de Sitter space is dual to a two-dimensional conformal field theory whose right-and left-moving central charges are given by cR = 24k and cL = 0, respectively, being k the level of the Chern-Simons action. We study the classical theory both at the linear and non-linear level. In particular, we show how Chiral Gravity is included as a special sector. In addition, the theory has other sectors, which we explore; we exhibit analytic exact solutions that are not solutions of Topologically Massive Gravity (and, consequently, neither of General Relativity) and still satisfy Brown-Henneaux asymptotically AdS3 boundary conditions.

2 + 1 EINSTEIN GRAVITY AS A DEFORMED CHERN-SIMONS THEORY

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.

Higher Gauge Theory and Gravity in 2+1 Dimensions

International Journal of Modern Physics A, 2007

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black...

The Canonical Exterior Formulation for the Topologically (2+1) Massive Gravity Theory

2007

The canonical covariant formalism (CCF) for the topologically mas- sive theory in (2+1) dimensions is constructed. The theory is formulated on the exterior algebra, then is naturally invariant under coordinates transformations or diffeomorphisms. This model containing the Chern- Simons terms is a higher derivative one, so in order to define canonical momenta the Ostrogradski transformation is introduced. Starting from the first order CCF, we find the second order canonical vierbein formal- ism (CVF). The primary constraints obtained in the CCF are analyzed. In the framework of the second order CVF the new constraints were found. From the Hamiltonian density obtained in the CCF and by making the space-time decomposition, the proper Hamiltonian in the CVF is constructed. This is the correct Hamiltonian which generates the time evolution of generic functional of fields and momenta. Mathematics Subject Classification: 70S05, 70H45, 83C80

Charged Black Holes in Three Dimensional Einstein Theory with Torsion and Chern Simons Terms

2009

We study the three-dimensional gravity with torsion given by the Mielke-Baekler (MB) model coupled to gravitational Chern-Simons term, and that possess electric charge described by Maxwell-Chern-Simons electrodynamics. We find and discuss this theory's charged black holes solutions and uncharged solutions. We find that for vanishing torsion our solutions by means of a coordinate transformation can be written as three-dimensional Chern-Simons black holes. We also discuss a special case of this theory, Topologically Massive Gravity (TMG) at chiral point, and we show that the logarithmic solution of TMG is also a solution of the MB model at a fixed point in the space of parameters. Furthermore, we show that our solutions generalize Godel type solutions in a particular case. Also, we recover BTZ black hole in Riemann-Cartan spacetime for vanishing charge.

The Gravitational Behaviour of an Effective Topological Field Theory

2014

Effective topological field theories describe the topological properties of Dirac fermions in the low-energy regime. In this work, we consider fermions coupled to a SO(5) Cartan connection on suitable four-dimensional compact manifolds. We show that the corresponding effective topological field theory, suitably constrained on the basis of topological motivations, gives rise to a gravitational action with a cosmological constant and Barbero-Immirzi parameter which is compatible, at classical level, with the vacuum general relativity.

Topological gravity with non-compact matter

Journal of High Energy Physics, 2019

We couple twisted non-compact N = (2, 2) supersymmetric models to topological gravity in two dimensions. We propose expressions for the genus zero correlation functions based on a Kadomtsev-Petviashvili integrable hierarchy. Moreover, we prove recursion relations satisfied by the topological gravity amplitudes at all genera and compute characteristic critical exponents. We discuss the extent to which moving beyond the N = 2 central charge barrier opens a window on two-dimensional gravity with central charge larger than one.