Towards an exact frame formulation of conformal higher spins in three dimensions

In this note we discuss some aspects of the frame formulation of conformal higher spins in three dimensions. We give some exact formulae for the coupled spin two - spin three part of the full higher spin theory and propose a star product Lagrangian for all spins from two and up. Since there is no consistent Lagrangian formulation based on the Poisson bracket we start the construction from the field equations in this approximation of the star product. The higher spin algebra is then realized in terms of classical variables which leads to certain important simplifications that we take advantage of. The suggested structure of the all-spin Lagrangian given here is, however, obtained using an expansion of the star product beyond the Poisson bracket in terms of multi-commutators and the Lagrangian should be viewed as a starting point for the derivation of the full theory based on a star product. How to do this is explained as well as how to include the coupling to scalar fields. We also comment on the AdS/CFT relation to four dimensions.Comment: 18 pages, v2: misprints corrected, an appendix, footnotes and some clarifying remarks added, 21 page

On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field

We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. Both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. Explicit expressions for the source terms are suggested and subjected to some simple tests. We also discuss a cascading relation between the Chern-Simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 Chern-Simons action in terms of the spin connection expressed in terms of the frame field. This cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.Comment: v2: 20 pages, misprints corrected, footnotes adde

Butterfly Optics Exceed the Theoretical Limits of Conventional Apposition Eyes

Optical experiments on butterfly compound eyes show that they have angular sensitivities narrower than expected from conventional apposition eyes. This superior performance is explained by a theoretical model where the cone stalk is considered as a modecoupling device. In this model the Airy diffraction pattern of the corneal facet excites a combination of the two waveguide modes LP01 and LP02. When the two modes propagate through the cone stalk the power of LP02 is transferred to LP01 alone which is supported by the rhabdom. This mechanism produces a higher on-axis sensitivity and a narrower angular sensitivity than conventional apposition optics. Several predictions of the model were confirmed experimentally.

Empirical multi-wavelength prediction method for very high energy gamma-ray emitting BL Lacs

Aim: We have collected the most complete multi-wavelength ($6.0 - 6.0 \times 10^{-18} cm$) dataset of very high energy (VHE) $\gamma$-ray emitting (TeV) BL Lacs, which are the most numerous extragalactic VHE sources. Using significant correlations between different bands, we aim to identify the best TeV BL Lac candidates that can be discovered by the current and next generation of imaging air Cherenkov telescopes. Methods: We formed five datasets from lower energy data, i.e. radio, mid-infrared, optical, X-rays, and GeV $\gamma$-ray, and five VHE $\gamma$-ray datasets to perform a correlation study between different bands and to construct the prediction method. The low energy datasets were averaged for individual sources, while the VHE $\gamma$-ray data were divided into subsets according to the flux state of the source. We then looked for significant correlations and determined their best-fit parameters. Using the best-fit parameters we predicted the level of VHE $\gamma$-ray flux for a sample of 182 BL Lacs, which have not been detected at TeV energies. We identified the most promising TeV BL Lac candidates based on the predicted VHE $\gamma$-ray flux for each source. Results: We found 14 significant correlations between radio, mid-infrared, optical, $\gamma$-ray, and VHE $\gamma$-ray bands. The correlation between optical and VHE $\gamma$-ray luminosity is established for the first time. We attribute this to the more complete sample and more accurate handling of host galaxy flux in our work. We found nine BL Lac candidates whose predicted VHE $\gamma$-ray flux is high enough for detection in less than 25 hours with current imaging air Cherenkov telescopes.Comment: 10 pages, 2 figures, 4 Table

A Note on Topological M5-branes and String-Fivebrane Duality

We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.Comment: 11 pp, plain te

On relating multiple M2 and D2-branes

Due to the difficulties of finding superconformal Lagrangian theories for multiple M2-branes, we will in this paper instead focus on the field equations. By relaxing the requirement of a Lagrangian formulation we can explore the possibility of having structure constants $f^{ABC}{}_D$ satisfying the fundamental identity but which are not totally antisymmetric. We exemplify this discussion by making use of an explicit choice of a non-antisymmetric $f^{ABC}{}_D$ constructed from the Lie algebra structure constants $f^{ab}{}_c$ of an arbitrary gauge group. Although this choice of $f^{ABC}{}_D$ does not admit an obvious Lagrangian description, it does reproduce the correct SYM theory for a stack of $N$ D2-branes to leading order in $g_{YM}^{-1}$ upon reduction and, moreover, it sheds new light on the centre of mass coordinates for multiple M2-branes.Comment: 9 pages, references added and statements concerning the fundamental identity revise

An action for the super-5-brane in D=11 supergravity

An alternative path is taken for deriving an action for the supersymmetric 5-brane in 11 dimensions. Selfduality does not follow from the action, but is consistent with the equations of motion for arbitrary supergravity backgrounds. The action involves a 2-form as well as a 5-form world-volume potential; inclusion of the latter makes the action, as well as the non-linear selfduality relation for the 3-form field strength, polynomial. The requirement of invariance under kappa-transformations determines the form of the selfduality relation, as well as the action. The formulation is shown to be equivalent to earlier formulations of 5-brane dynamics.Comment: plain tex, 8pp. Essential correction to the selfduality equation. Added paragraph showing equivalence to other formulation

The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections

We solve the superspace Bianchi identities for ten-dimensional supersymmetric Yang-Mills theory without imposing any kind of constraints apart from the standard conventional one. In this way we obtain a set of algebraic conditions on certain fields which in the on-shell theory are constructed as composite ones out of the physical fields. These conditions must hence be satisfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory (as well as the fields) are identified as elements of a certain spinorial cohomology, giving control over field redefinitions and the distinction between physically relevant higher-order corrections and those removable by field redefinitions. The conditions derived severely constrain theories involving F^2-level terms plus higher-order corrections, as for instance those derived from open strings as effective gauge theories on D-branes.Comment: plain tex, 18 pp., 3 fig