Dimensional Chern-Simons Gravity Research Articles

Non-relativistic gravity theory based on an enlargement of the extended Bargmann algebra

In this work we study a non-relativistic three dimensional Chern-Simons gravity theory based on an enlargement of the Extended Bargmann algebra. A finite nonrelativistic Chern-Simons gravity action is obtained through the non-relativistic contraction of a particular U(1) enlargement of the so-called AdS-Lorentz algebra. We show that the non-relativistic gravity theory introduced here reproduces the Maxwellian Exotic Bargmann gravity theory when a flat limit ℓ → ∞ is applied. We also present an alternative procedure to obtain the non-relativistic versions of the AdS-Lorentz and Maxwell algebras through the semigroup expansion method.

A generalized action for (2 + 1)-dimensional Chern–Simons gravity

We show that the so-called semi-simple extended Poincaré (SSEP) algebra in D dimensions can be obtained from the anti-de Sitter algebra by means of the S-expansion procedure with an appropriate semigroup S. A general prescription is given for computing Casimir operators for S-expanded algebras, and the method is exemplified for the SSEP algebra. The S-expansion method also allows us to extract the corresponding invariant tensor for the SSEP algebra, which is a key ingredient in the construction of a generalized action for Chern–Simons gravity in (2 + 1) dimensions.

Even-dimensional topological gravity from Chern–Simons gravity

It is shown that the topological action for gravity in 2n-dimensions can be obtained from the (2n+1)-dimensional Chern–Simons gravity genuinely invariant under the Poincaré group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)-dimensional Chern–Simons gravity theory with suitable boundary conditions.The field ϕa, which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d−1,1).

First law of black ring thermodynamics in higher dimensional Chern-Simons gravity

The physical process version and the equilibrium state version of the first law of black ring thermodynamics in n-dimensional Einstein gravity with Chern-Simons term were derived. This theory constitutes the simplest generalization of the five-dimensional one admitting a stationary black ring solution. The equilibrium state version of the first law of black ring mechanics was achieved by choosing any cross section of the event horizon to the future of the bifurcation surface.

Topological Ward identity and anti-de Sitter space/CFT correspondence

The dual relationship between the supergravity in the anti-de Sitter (AdS) space and the superconformal field theory is discussed in the simplest form. We show that a topological Ward identity holds in the three dimensional Chern–Simons gravity. In this simple case the proposed dual relationship can be understood as the topological Ward identity. Extensions to the supersymmetric theories and higher dimensional ones are also briefly discussed.

Wilson loops and black holes in 2+1 dimensions

In 2+1 dimensional Chern-Simons gravity, Wilson loops in the three dimensional Anti de Sitter group, SO(2,2), reproduce the spinning black hole of Bañados, Teitelboim and Zanelli (BTZ) by naturally duplicating the necessary identification of points of a four dimensional globally SO(2,2) invariant space in which the hole appears as an embedding.

Erratum: (2+1)-dimensional Chern-Simons gravity as a Dirac square root

For (2+1)-dimensional spacetimes with the spatial topology of a torus, the transformation between the Chern-Simons and ADM versions of quantum gravity is constructed explicitly, and the wave functions are compared. It is shown that Chern-Simons wave functions correspond to modular forms of weight 1/2, that is, spinors on the ADM moduli space, and that their evolution (in York's ``extrinsic time'' variable) is described by a Dirac equation. (This version replaces paper 9109006, which was garbled by my mailer.)

(1+1)-dimensional gravity through a dimensional reduction

The GL(2, R ) gauge theory of (1+1)-dimensional gravity, which contains the Jackiw-Teitelboim model and the dilaton gravity model as special cases, is derived as a dimensional reduction of a (2+1)-dimensional Chern-Simons gravity based on the gauge group SO(3, 1)⊗GL(1, R ).

(2+1)-dimensional Chern-Simons gravity as a Dirac square root.

For simple enough spatial topologies, at least four approaches to (2+1)-dimensional quantum gravity have been proposed: Wheeler-DeWitt quantization, canonical quantization in Arnowitt-Deser-Misner (ADM) variables on reduced phase space, Chern-Simons quantization, and quantization in terms of Ashtekar-Rovelli-Smolin loop variables. An important problem is to understand the relationships among these approaches. By explicitly constructing the transformation between the Chern-Simons and ADM Hilbert spaces, we show here that Chern-Simons quantization naturally gives rise to spinorial wave functions on superspace, whose time evolution is governed by a Dirac equation. Chern-Simons quantum gravity can therefore be interpreted as the Dirac square root of the Wheeler-DeWitt equation.

Scattering in (2 + 1)-dimensional Chern-Simons supergravity

We discuss the problem of two-superparticle scattering in the framework of (2 + 1)-dimensional gauge theory of N = 2 Poincaré supergravity coupled to point sources. Our approach is the extension of our previous work for the case of (2 + 1)-dimensional Chern-Simons gravity, in which one of the particle is treated as a test particle scattering in the gravitational field of the other. We show that to relate the classical phase space of the particles to their space-time coordinates and momenta, it is necessary to take the gauge group to be the universal covering group of the N = 2 Poincaré supergroup. We also show that in the test particle approach, one of the superparticles is effectively a spinless particle. We explicitly calculate the corresponding scattering amplitude.