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Register a new userTopologically massive gravity and complex Chern-Simons terms
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This paper is withdrawn because its results have been previously reported in arxiv hep-th/0507200.
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We obtain a family of $pp$-wave solutions of Minimal Massive 3d Gravity (MMG) minimally coupled with the Maxwell-Chern-Simons theory. The simultaneous solutions of the MMG and the Maxwell field equations require that the Maxwell field should satisfy an anti-self-duality condition.
We define and discuss classical and quantum gravity in 2+1 dimensions in the Galilean limit. Although there are no Newtonian forces between massive objects in (2+1)-dimensional gravity, the Galilean limit is not trivial. Depending on the topology of spacetime there are typically finitely many topological degrees of freedom as well as topological interactions of Aharonov-Bohm type between massive objects. In order to capture these topological aspects we consider a two-fold central extension of the Galilei group whose Lie algebra possesses an invariant and non-degenerate inner product. Using this inner product we define Galilean gravity as a Chern-Simons theory of the doubly-extended Galilei group. The particular extension of the Galilei group we consider is the classical double of a much studied group, the extended homogeneous Galilei group, which is also often called Nappi-Witten group. We exhibit the Poisson-Lie structure of the doubly extended Galilei group, and quantise the Chern-Simons theory using a Hamiltonian approach. Many aspects of the quantum theory are determined by the quantum double of the extended homogenous Galilei group, or Galilei double for short. We study the representation theory of the Galilei double, explain how associated braid group representations account for the topological interactions in the theory, and briefly comment on an associated non-commutative Galilean spacetime.
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 asymptotic Anti-deSitter behavior. For constant or fixed Weyl factor our results agree with a suitable scaling limit of topologically massive gravity results. For varying Weyl factor we find an enhancement of the asymptotic symmetry group, the details of which depend on certain choices. We focus on a particular example where an affine u(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a free chiral boson in the dual conformal field theory.
We construct a manifestly covariant differential Noether charge for theories with Chern-Simons terms in higher dimensional spacetimes. This is in contrast to Tachikawas extension of the standard Lee-Iyer-Wald formalism which results in a non-covariant differential Noether charge for Chern-Simons terms. On a bifurcation surface, our differential Noether charge integrates to the Wald-like entropy formula proposed by Tachikawa in arXiv:hep-th/0611141.
The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of operators that splits the fundamental fields according to their individual degrees of freedom. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes gets a new insight. Our conclusion is that the only tachyon- and ghost-free model is the Einstein-Hilbert action added up by the Chern-Simons term with a time-like vector of the type $v^{mu} = (mu,vec{0})$. Spectral consistency imposes taht the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to usual gauge theories whenever conditions for suppression of tachyons and ghosts are required.
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