The Five Interior Powers

Spiritual Updat

Renormalization Group Flow in Scalar-Tensor Theories. II

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in $d=4$ for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in $d=4$ including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.Comment: 14 pages. v.2: Minor changes, some references adde

The economics of defence in France and the UK

France and the UK face similar geostrategic circumstances: both were once Great Powers and still retain their positions among the five permanent members of the UN Security Council. During the Cold War both were dwarfed by the super-powers and were thus extremely sensitive about their status: what the French called their grandeur and the British called their seat at the top table. Despite their strategic similarities, they have differed in many of their defence policy choices and in particular how they balanced their strategic aspirations with their limited financial resources. Thus a comparison of British and French defence policies provides a revealing case study of military choices

Reconstruction of the primordial fluctuation spectrum from the five-year WMAP data by the cosmic inversion method with band-power decorrelation analysis

The primordial curvature fluctuation spectrum is reconstructed by the cosmic inversion method using the five-year WMAP data of the cosmic microwave background temperature anisotropy. We apply the covariance matrix analysis and decompose the reconstructed spectrum into statistically independent band-powers. The statistically significant deviation from a simple power-law spectrum suggested by the analysis of the first-year data is not found in the five-year data except possibly at one point near the border of the wavenumber domain where accurate reconstruction is possible.Comment: 9page

Laurent series expansion of sunrise-type diagrams using configuration space techniques

We show that configuration space techniques can be used to efficiently calculate the complete Laurent series \eps-expansion of sunrise-type diagrams to any loop order in D-dimensional space-time for any external momentum and for arbitrary mass configurations. For negative powers of \eps the results are obtained in analytical form. For positive powers of \eps including the finite \eps^0 contribution the result is obtained numerically in terms of low-dimensional integrals. We present general features of the calculation and provide exemplary results up to five loop order which are compared to available results in the literature.Comment: 20 pages, 3 eps-figures include

Open Spinning Strings

We find classical open string solutions in the AdS_5\times S^5/\Zop_2 orientifold with angular momenta along the five-sphere. The energy of these solutions has an expansion in integral powers of $\lambda$ with sigma-model corrections suppressed by inverse powers of $J$ - the total angular momentum. This gives a prediction for the exact anomalous dimensions of operators in the large $N$ limit of an ${\cal N}=2$ $Sp(N)$ Super-Yang-Mills theory with matter. We also find a simple map between open and closed string solutions. This gives a prediction for an all-loop planar relationship between the anomalous dimensions of single-trace and two-quark operators in the dual gauge theory

Primary electric power generation systems for advanced-technology engines

The advantages of the all electric airplane are discussed. In the all electric airplane the generator is the sole source of electric power; it powers the primary and secondary flight controls, the environmentals, and the landing gear. Five candidates for all electric power systems are discussed and compared. Cost benefits of the all electric airplane are discussed