Higher Dimensional Chern-Simons Research Articles

Abelian tensor hierarchy in 4D, N = 1 superspace

With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.

Covariant Noether charge for higher dimensional Chern-Simons terms

We construct a manifestly covariant differential Noether charge for theories with Chern-Simons terms in higher dimensional spacetimes. This is in contrast to Tachikawa's 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.

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.

Gauging Away the Strong CP Problem

We propose a new solution to the strong-CP problem. It involves the existence of an unbroken gauged $U(1)_X$ symmetry whose gauge boson gets a Stuckelberg mass term by combining with a pseudoscalar field $\eta (x)$. The latter has axion-like couplings to $F_{QCD}\wedge F_{QCD}$ so that the theta parameter may be gauged away by a $U(1)_X$ gauge transformation. This system leads to mixed gauge anomalies and we argue that they are cancelled by the addition of an appropriate Wess-Zumino term, so that no SM fermions need to be charged under $U(1)_X$. We discuss scenarios in which the above set of fields and couplings appear. The mechanism is quite generic, but a natural possibility is that the the $U(1)_X$ symmetry arises from bulk gauge bosons in theories with extra dimensions or string models. We show that in certain D-brane Type-II string models (with antisymmetric tensor field strength fluxes) higher dimensional Chern-Simons couplings give rise to the required D=4 Wess-Zumino terms upon compactification. In one of the possible string realizations of the mechanism the $U(1)_X$ gauge boson comes from the Kaluza-Klein reduction of the eleven-dimensional metric in M-theory.

The physics of higher-dimensional Chern-Simons supergravities

Abstract We review some recent work on the physics underlying higher-dimensional Chern-Simons theories. By definition, the off-shell field content of 5d Chern-Simons supergravity is the same as that of standard supergravity. The equations of motion, however, are very different. One may expect that expanding the Chern-Simons equations around the most symmetrical vacuum may give supergravity (to some order) but this is not the case. We argue here that an intriguing connection between both theories may exist, at least asymptotically (far away from sources), and the key role is played by symmetry breaking. This is the written version of an invited talk delivered at the Conference Renormalization Group and Anomalies in Gravity and Cosmology, Ouro Preto, March 2003.

Gravitons and gauge fields in 5d Chern-Simons supergravity

Despite the nice geometrical properties of higher dimensional Chern-Simons (CS) supergravity theories these actions suffer from one major drawback, namely, their connection with the real world. After some quick remarks on three-dimensional gravity, we consider five-dimensional CS supergravity and study to what extend this theory reproduces the standard low energy description of gravitons and gauge fields. We point out that if one deforms the CS action by changing the value of the cosmological constant by a small amount (thus breaking the CS symmetry), propagation around AdS becomes non-trivial, asymptotically Schwarzschild-AdS solutions exist, and the gauge field acquires its standard quadratic propagator.

Dynamical structure of four-dimensional Chamseddine’s gauge theory of gravity

We perform the Dirac Hamiltonian analysis of a four-dimensional gauge theory of gravity with an action of the topological type, which generalizes some well-known two-dimensional models. We show that, in contrast with the two-dimensional case, the theory has a nonvanishing number of dynamical degrees of freedom and that its structure is very similar to higher-dimensional Chern-Simons gravity.

The dynamical structure of higher dimensional Chern-Simons theory

Higher dimensional Chern-Simons theorìes, even though constructed along the same topological pattern as in 2 + 1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G × U(1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion.