Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

Resonant Scattering and Recombination in CAL 87

The eclipsing supersoft X-ray binary CAL 87 has been observed with Chandra on August 13/14, 2001 for nearly 100 ksec, covering two full orbital cycles and three eclipses. The shape of the eclipse light curve derived from the zeroth-order photons indicates that the size of the X-ray emission region is about 1.5 solar radii. The ACIS/LETG spectrum is completely dominated by emission lines without any noticeable continuum. The brightest emission lines are significantly redshifted and double-peaked, suggestive of emanating in a 2000 km/s wind. We model the X-ray spectrum by a mixture of recombination and resonant scattering. This allows us to deduce the temperature and luminosity of the ionizing source to be kT = 50-100 eV and L_X = 5E37 erg/s.Comment: To appear in Proceedings of IAU Coll. 194 "Compact binaries in the Galaxy and beyond" (Rev. Mex. A&A Conf. Series), eds. G. Tovmassian and E. Sio

A Representation of Symmetry Generators for the Type IIB Superstring on a Plane Wave in the U(4) Formalism

We calculate the symmetry currents for the type IIB superstring on a maximally supersymmetric plane wave background using the N=(2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N=(2,2) worldsheet fields. Because the action is no longer quadratic, we use a light-cone version to display the currents in terms of the covariant worldsheet variables.Comment: 9 pages, harvmac, Corrected some typographical errors, Added reference

How strong is the evidence for accelerated expansion?

We test the present expansion of the universe using supernova type Ia data without making any assumptions about the matter and energy content of the universe or about the parameterization of the deceleration parameter. We assume the cosmological principle to apply in a strict sense. The result strongly depends on the data set, the light-curve fitting method and the calibration of the absolute magnitude used for the test, indicating strong systematic errors. Nevertheless, in a spatially flat universe there is at least a 5 sigma evidence for acceleration which drops to 1.8 sigma in an open universe.Comment: 16 pages, 3 figure

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.Comment: 31 pages, harvmac (b); minor correction

QP-Structures of Degree 3 and 4D Topological Field Theory

A A BV algebra and a QP-structure of degree 3 is formulated. A QP-structure of degree 3 gives rise to Lie algebroids up to homotopy and its algebraic and geometric structure is analyzed. A new algebroid is constructed, which derives a new topological field theory in 4 dimensions by the AKSZ construction.Comment: 17 pages, Some errors and typos have been correcte

On Duality in the Born-Infeld Theory

The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with non-trivial backgroud fields in four dimensions is established. This construction is carried out in detail by analysing the hamiltonian structure of the Born-Infeld theory. The equivalence with the usual Born-Infeld theory is shown.Comment: revtex, 4 page

The spectroscopic evolution of the recurrent nova T Pyxidis during its 2011 outburst. II.The optically thin phase and the structure of the ejecta in recurrent novae

We continue our study of the physical properties of the recurrent nova T Pyx, focussing on the structure of the ejecta in the nebular stage of expansion during the 2011 outburst. The nova was observed contemporaneously with the Nordic Optical Telescope (NOT), at high resolution spectroscopic resolution (R ~ 65000) on 2011 Oct. 11 and 2012 Apr. 8 (without absolute flux calibration), and with the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope, at high resolution (R ~ 30000) on 2011 Oct. 10 and 2012 Mar. 28 (absolute fluxes). We use standard plasma diagnostics (e.g. [O III] and [N II] line ratios and the H$\beta$ line fluxes) to constrain electron densities and temperatures. Using Monte Carlo modeling of the ejecta, we derive the structure and filling factor from comparisons to the optical and ultraviolet line profiles. The ejecta can be modeled using an axisymmetric conical -- bipolar -- geometry with a low inclination of the axis to the line of sight, i=15+/-5 degrees, compatible with published results from high angular resolution optical spectro-interferometry. The structure is similar to that observed in the other short orbital period recurrent novae during their nebular stages. We show that the electron density scales as $t^{-3}$ as expected from a ballistically ejected constant mass shell; there is no need to invoke a continuing mass outflow following the eruption. The derived mass for the ejecta with filling factor f ~ 3%, M_ej ~ 2E-6$M_sun is similar to that obtained for other recurrent nova ejecta but inconsistent with the previously reported extended optically thick epoch of the explosion. We suggest that the system underwent a common envelope phase following the explosion that produced the recombination event. Implications for the dynamics of the recurrent novae are discussed. (truncated)Comment: accepted for publication in A&A (10 Nov. 2012), 10 pgs, 16 fig

Driven depinning of strongly disordered media and anisotropic mean-field limits

Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the driving force and that slip along at least one of the directions transverse to the motion. A realization of such a model is a collection of elastic channels with transverse viscous couplings. In the infinite range limit this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special cases of the generic model.Comment: 4 pages, 2 figure