N=4, d=3 nonlinear electrodynamics

We construct a new off-shell $\mathcal{N}{=}4$, $d{=}3$ nonlinear vector supermultiplet. The irreducibility constraints for the superfields leave in this supermultiplet the same component content as in the ordinary linear vector supermultiplet. We present the most general sigma-model type action for the $\mathcal{N}{=}4$, $d{=}3$ electrodynamics with the nonlinear vector supermultiplet, which despite the nonlinearity of the supermultiplet may be written as an integral over a chiral superspace. This action share the most important properties with its linear counterpart. We also perform the dualization of the vector component into a scalar one and find the corresponding $\mathcal{N}{=}4$, $d{=}3$ supersymmetric action which describes new hyper-K\"ahler sigma-model in the bosonic sector.Comment: 8 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-

New massive gravity, extended

We consider gravity in three dimensions with an arbitrary number of curvature corrections. We show that such corrections are always functions of only three independent curvature invariants. Demanding the existence of a holographic c-theorem we show how to fix the coefficients in the action for an arbitrarily high order, recovering the new massive gravity lagrangian at quadratic order. We calculate the central charge $c$ and show that using Cardy's formula it matches the entropy of black hole solutions, which we construct. We also consider fluctuations about an AdS background, and find that it is possible to obtain two derivative equations by imposing a single constraint, thereby lifting the pathologic massive modes of new massive gravity. If we do not impose this, there is a set of ghosty massive modes propagating in the bulk. However, at $c=0$ these become massless and it is expected that these theories encode the dynamics of the spin two sector of strongly coupled logarithmic CFT's.Comment: 4 page

Attractors and first order formalism in five dimensions revisited

The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five dimensional rotating black object potential depending on Taub-NUT, electric and magnetic charges as well as on all the scalar and gauge fields, is investigated. The first order formalism in d=5 is constructed and analyzed. We derive a general expression defining the fake superpotential which is valid for all charge configurations. An explicit expression for the fake superpotential is constructed, for all very special geometries, in the case of vanishing Taub-NUT charge. We carry out an analogous construction in the very special geometries corresponding to $t^3$ and $stu$ models, for the most general charge configurations. The attractor flows and horizon values of all fields are given.Comment: 33 pages, PACS numbers: 04.65.+e, 04.50.Gh, 04.70.Bw, 04.70.Dy, keywords: five dimensional supergravity, black objects, entropy, attractor flows, first order formalism, fake superpotential. Several typos corrected; one reference added; section 6 (conclusions) expande