Special geometry and symplectic transformations

Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity, and $n$ complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an $(n+1)$-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic $(2n)$- or $(2n+2)$-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.Comment: 11 pages, latex using espcrc2, no figures. Some factors and minor corrections. Version to be published in the proceedings of the Spring workshop on String theory, Trieste, April 199

The N=2 Super Yang-Mills Low-Energy Effective Action at Two Loops

We have carried out a two loop computation of the low-energy effective action for the four-dimensional N=2 supersymmetric Yang-Mills system coupled to hypermultiplets, with the chiral superfields of the vector multiplet lying in an abelian subalgebra. We have found a complete cancellation at the level of the integrands of Feynman amplitudes, and therefore the two loop contribution to the action, effective or Wilson, is identically zero.Comment: 8 pages, Latex, 2 .eps figure

Consistent truncation of d = 11 supergravity on AdS_4 x S^7

We study the system of equations derived twenty five years ago by B. de Wit and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7) symmetry, we determine the most general solution to this system at each point on the coset space E_7(7)/SU(8). We show that invariants of the general solution are given by the fluxes in eleven-dimensional supergravity. This allows us to both clarify the explicit non-linear ansatze for the fluxes given previously and to fill a gap in the original proof of the consistent truncation. These results are illustrated with several examples.Comment: 41 pages, typos corrected, published versio

M Theory As A Matrix Model: A Conjecture

We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = infinity limit of the supersymmetric matrix quantum mechanics describing D0-branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity . The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.Comment: Typo and tex error corrected. 41 pages, harvma

AMBER and CRIRES observations of the binary sgB[e] star HD 327083: evidence of a gaseous disc traced by CO bandhead emission

HD 327083 is a sgB[e] star that forms a binary system with an orbital semi-major axis of ~1.7 AU. Our previous observations using the VLTI and AMBER in the medium resolution K-band mode spatially resolved the environment of HD 327083. The continuum visibilities obtained indicate the presence of a circumbinary disc. CO bandhead emission was also observed. However, due to the limited spectral resolution of the previous observations, the kinematic structure of the emitting material was not constrained. In this paper, we address this and probe the source of the CO emission with high spectral resolution and spatial precision. We have observed HD 327083 with high spectral resolution (25 & 6 km/s) using AMBER and CRIRES. The observations are compared to kinematical models to constrain the source of the emission. It is shown that the CO bandhead emission can be reproduced using a model of a Keplerian disc with an inclination and size consistent with our previous VLTI observations. The model is compared to AMBER differential phase measurements, which have a precision as high as 30-micro-arcseconds. A differential phase signal corresponding to 0.15 milli-arcseconds (~5 sigma) is seen over the bandhead emission, which is in excellent agreement with the model that fits the CRIRES observations. In comparison, a model of an equatorial outflow, as envisaged in the standard sgB[e] scenario, does not reproduce the observations well. The excellent agreement between the disc model and observations in the spatial and spectral domains is compelling evidence that the CO bandhead emission of HD 327083 originates in a circumbinary Keplerian disc. In contrast, the model of an equatorial outflow cannot reproduce the observations well. This suggests that the standard sgB[e] scenario is not applicable to HD 327083, which supports the hypothesis that the B[e] behaviour of HD 327083 is due to binarity (ABRIDGED).Comment: Accepted for publication in A&

Completeness in supergravity constructions

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler manifold defines a complete quaternionic Kahler manifold of negative scalar curvature. We classify all complete quaternionic Kahler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.Comment: 29 page

On BPS bounds in D=4 N=2 gauged supergravity II: general matter couplings and black hole masses

We continue the analysis of BPS bounds started in arXiv:1110.2688, extending it to the full class of N=2 gauged supergravity theories with arbitrary vector and hypermultiplets. We derive the general form of the asymptotic charges for asymptotically flat (M_4), anti-de Sitter (AdS_4), and magnetic anti-de Sitter (mAdS_4) spacetimes. Some particular examples from black hole physics are given to explicitly demonstrate how AdS and mAdS masses differ when solutions with non-trivial scalar profiles are considered.Comment: 21 pages; v2 added reference, published version; v3 minor correction

N=2 Conformal Superspace in Four Dimensions

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.Comment: 43 pages; v2 references added, acknowledgments update

Explaining nascent entrepreneurship across countries

This paper aims at explaining cross-country variation in nascent entrepreneurship. Regression analysis is applied using various explanatory variables derived from three different approaches. We make use of the Global Entrepreneurship Monitor database, including nascent entrepreneurship rates for 36 countries in 2002 as well as variables from standardized national statistics. The first approach relates the level of entrepreneurship of a country to its level of economic development. We found evidence for a U-shaped relationship. The second approach deals with a regime switch where the innovative advantage moves from large, established enterprises to small and new firms, because new technologies have reduced the importance of scale economies in many sectors. The third approach assumes that nascent entrepreneurship depends upon aggregate conditions such as technology, demography, culture and institutions, influencing opportunities, resources, skills and preferences. Several indicators of these aggregate conditions are found to correlate with nascent entrepreneurship. A full model combining the three approaches includes a U-shaped relationship with per capita income as well as with Porter's innovative capacity index, in addition to effects of social security expenditure (-) and the total business ownership rate (+). Finally, a (former) communist-country dummy plays an important role.