A finite action principle for Chern-Simons AdS gravity is presented. The construction is carried out in detail first in five dimensions, where the bulk action is given by a particular combination of the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term; and is then generalized for arbitrary odd dimensions. The boundary term needed to render the action finite is singled out demanding the action to attain an extremum for an appropriate set of boundary conditions. The boundary term is a local function of the fields at the boundary and is sufficient to render the action finite for asymptotically AdS solutions, without requiring background fields. It is shown that the Euclidean continuation of the action correctly describes black hole thermodynamics in the canonical ensemble. Additionally, background independent conserved charges associated with the asymptotic symmetries can be written as surface integrals by direct application of Noether's theorem.1 A submanifold that satisfies this condition is also known as totally umbilical [20]

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.

The two published lithium peroxide structures, both ascribed to the hexagonal P6 space group, were subjected to reinterpretation, and another more symmetric structure, now belonging to the P6(3)/mmc space group, was found. Detailed density-functional quantum mechanical calculations and crystal structure optimizations were carried out on both structures and the energetic arguments obtained therewith helped to rule out one of them.

No abstract

The 5d electron-based Sr2−xLaxIrO4 system (0≤x≤0.2) has been synthesized by a solid-state route. The x = 0 composition is a nonmetallic weak ferromagnet with a Curie temperature at about 240 K. The crystal structure behaviour and magnetic properties exhibited by this Sr2−xLaxIrO4 system can be explained on the basis of the extended character of the 5d electrons of the Ir cation and its valence states. Rietveld analysis of x-ray powder diffraction on Sr2IrO4 agrees well with previous structural neutron experiments. Furthermore, density functional theory (DFT) calculations predict that I41/acd represents a more stable crystal structure than K2NiF4 (I4/mmm). Electrical resistivity and magnetic properties of Sr2−xLaxIrO4 are strongly dependent on the Ir3+ content. The Sr2−xLaxIrO4 magnetic behaviour in the range of 2–240 K can be ascribed to a weak ferromagnet, produced by an array of canted antiferromagnetically ordered Ir4+ magnetic moments.

Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics.Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times.In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge field curvature (field strength) for the AdS gauge group is asymptotically finite.For that purpose we consider an asymptotic expansion of the vielbein and spin connection that may be regarded as a perturbation of an AdS space-time, but allowing a non zero torsion.Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories.

This is the translation to appear in the "SUPERSYMMETRY 2000 -Encyclopaedic Dictionary" of the original Comptes Rendus Note, published in March 1980, in which basic notions of noncommutative geometry were introduced and applied to noncommutative tori. These include connections on finite projective modules, their curvature, and the Chern character. Finite projective modules on the noncommutative two-torus T 2 θ were realized as Schwartz spaces of vector valued functions on R. Explicit constant curvature connections were constructed and a basic integrality phenomenon of the total curvature was displayed. The pseudo-differential calculus and the Atiyah-Singer index theorems were extended to Lie group actions on C * algebras and used to explain the above integrality of the total curvature by an index formula for finite difference-differential operators on the line. Recent interest in the hep-th literature for basic notions of noncommutative geometry in the case of noncommutative tori (cf for instance hep-th/0012145 for an excellent review) prompted us to make the English translation of the original paper available.

The purpose of this Letter is to continue the study of the class of models proposed in the previous paper [1] hep-th/0002077. The model corresponds to a system of branes of diverse dimensionalities with Chern-Simons actions for a supergroup, embedded in a background described also by a Chern-Simons action. The model treats the background and the branes on an equal footing, providing a 'brane-target space democracy'. Here we suggest some possible extensions of the original model, and disscuss its equations of motion, as well as the issue of currents and charges carried by the branes. We also disscuss the relationship with M-theory and Superstring theory.