Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity

The conserved charges associated with gauge symmetries are defined at a boundary component of spacetime because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to lift the arbitrariness in the Hamiltonian framework. An alternative covariant formula was proposed by one of us for an arbitrary variation of the superpotential, it depends only on the equations of motion and on the gauge symmetry under consideration. Here we emphasize that in order to compute the charges, it is enough to stay at a boundary of spacetime, without requiring any hypothesis about the bulk or about other boundary components, so one may speak of holographic charges. It is well known that the asymptotic symmetries that lead to conserved charges are really defined at infinity, but the choice of boundary conditions and surface terms in the action and in the charges is usually determined through integration by parts, whereas each component of the boundary should be considered separately. We treat the example of gravity (for any spacetime dimension, with or without cosmological constant), formulated as an affine theory which is a natural generalization of the Palatini and Cartan-Weyl (vielbein) first-order formulations. We then show that the superpotential associated with a Dirichlet boundary condition on the metric (the one needed to treat asymptotically flat or AdS spacetimes) is the one proposed by Katz et al and not that of Komar. We finally discuss the KBL superpotential at null infinity

Physical constraints on interacting dark energy models

Physical limits on the equation-of-state (EoS) parameter of a dark energy component non-minimally coupled with the dark matter field are examined in light of the second law of thermodynamics and the positiveness of entropy. Such constraints are combined with observational data sets of type Ia supernovae, baryon acoustic oscillations and the angular acoustic scale of the cosmic microwave background to impose restrictions on the behaviour of the dark matter/dark energy interaction. Considering two EoS parameterisations of the type $w = w_0 + w_a\zeta(z)$, we derive a general expression for the evolution of the dark energy density and show that the combination of thermodynamic limits and observational data provide tight bounds on the $w_0 - w_a$ parameter space.Comment: 7 pages, 4 figures. Accepted for publication in European Physical Journal

Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets: I. Theory

We consider theoretically the effects of an applied uniform magnetic field on the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya layered quantum Heisenberg antiferromagnets. The first case is relevant for systems such as the two-dimensional square lattice antiferromagnet Sr(2)CuO(2)Cl(2), while the later is known to be relevant to the physics of the layered orthorhombic antiferromagnet La(2)CuO(4). We first establish the correspondence betwenn the low-energy spectrum obtained within the anisotropic non-linear sigma model and by means of the spin-wave approximation for a standard easy-axis antiferromagent. Then, we focus on the field-theory approach to calculate the magnetic field dependence of the magnon gaps and spectral intensities for magnetic fields applied along the three possible crystallographic directions. We discuss the various possible ground states and their evolution with temperature for the different field orientations, and the occurrence of spin-flop transitions for fields perpendicular to the layers (transverse fields) as well as for fields along the easy axis (longitudinal fields). Measurements of the one-magnon Raman spectrum in Sr(2)CuO(2)Cl(2) and La(2)CuO(4) and a comparison between the experimental results and the predictions of the present theory will be reported in part II of this research work [L. Benfatto et al., cond-mat/0602664].Comment: 21 pages, 11 figures, final version. Part II of the present work is presented in cond-mat/060266