Solution to the Ward Identities for Superamplitudes

Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and R-invariant form: it is expressed as a sum of very simple SUSY and SU(N)_R-invariant Grassmann polynomials, each multiplied by a "basis amplitude". For (Next-to)^K MHV n-point superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU(n-4) corresponding to the rectangular Young diagram with N columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of color-ordered single-trace amplitudes in N=4 gauge theory. We also analyze the more significant reduction that occurs in N=8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level.Comment: 29 pages, published versio

Escape from a zero current state in a one dimensional array of Josephson junctions

A long one dimensional array of small Josephson junctions exhibits Coulomb blockade of Cooper pair tunneling. This zero current state exists up to a switching voltage, Vsw, where there is a sudden onset of current. In this paper we present histograms showing how Vsw changes with temperature for a long array and calculations of the corresponding escape rates. Our analysis of the problem is based on the existence of a voltage dependent energy barrier and we do not make any assumptions about its shape. The data divides up into two temperature regimes, the higher of which can be explained with Kramers thermal escape model. At low temperatures the escape becomes independent of temperature.Comment: 4 pages 5 figure

Giant Backscattering Peak in Angle-Resolved Andreev Reflection

It is shown analytically and by numerical simulation that the angular distribution of Andreev reflection by a disordered normal-metal -- superconductor junction has a narrow peak at the angle of incidence. The peak is higher than the well-known coherent backscattering peak in the normal state, by a large factor G/G_0 (where G is the conductance of the junction and G_0=2e^2/h). The enhanced backscattering can be detected by means of ballistic point contacts.Comment: Instituut-Lorentz, Leiden, The Netherlands, 4 pages, REVTeX-3.0, 3 figure

Macroscopic Quantum Tunneling of a Fluxon in a Long Josephson Junction

Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.Comment: 30 pages LaTeX including 11 PS figures, using jpsj.sty. To be published on J. Phys. Soc. Jpn. Overestimates for damping amplitude is correcte

Random matrix theory, the exceptional Lie groups, and L-functions

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are here extended to non-classical groups. We focus on an explicit example: the exceptional Lie group G_2. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G_2, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the 7-dimensional representation of G_2. The random matrix calculations extend to all exceptional Lie groupsComment: 14 page

General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory

We evaluate all split helicity gluon tree amplitudes in open twistor string theory. We show that these amplitudes satisfy the BCFW recurrence relations restricted to the split helicity case and, hence, that these amplitudes agree with those of gauge theory. To do this we make a particular choice of the sextic constraints in the link variables that determine the poles contributing to the contour integral expression for the amplitudes. Using the residue theorem to re-express this integral in terms of contributions from poles at rational values of the link variables, which we determine, we evaluate the amplitudes explicitly, regaining the gauge theory results of Britto et al.Comment: 30 pages, minor misprints correcte

HAT-P-47b AND HAT-P-48b: Two Low Density Sub-Saturn-Mass Transiting Planets on the Edge of the Period--Mass Desert

We report the discovery of two new transiting extrasolar planets orbiting moderately bright (V = 10.7 and 12.2 mag) F stars (masses of 1.39 Msun and 1.10 Msun, respectively). The planets have periods of P = 4.7322 d and 4.4087 d, and masses of 0.21 MJ and 0.17 MJ which are almost half-way between those of Neptune and Saturn. With radii of 1.31 RJ and 1.13 RJ, these very low density planets are the two lowest mass planets with radii in excess that of Jupiter. Comparing with other recent planet discoveries, we find that sub-Saturns (0.18MJ < Mp < 0.3MJ) and super-Neptunes (0.05MJ < Mp < 0.18MJ) exhibit a wide range of radii, and their radii exhibit a weaker correlation with irradiation than higher mass planets. The two planets are both suitable for measuring the Rossiter-McLaughlin effect and for atmospheric characterization. Measuring the former effect would allow an interesting test of the theory that star-planet tidal interactions are responsible for the tendency of close-in giant planets around convective envelope stars to be on low obliquity orbits. Both planets fall on the edge of the short period Neptunian desert in the semi-major axis-mass plane.Comment: Submitted to AAS Journal

HATS-8b: A Low-Density Transiting Super-Neptune

HATS-8b is a low density transiting super-Neptune discovered as part of the HATSouth project. The planet orbits its solar-like G dwarf host (V=14.03 $\pm$ 0.10 and T$_{eff}$ =5679 $\pm$ 50 K) with a period of 3.5839 d. HATS-8b is the third lowest mass transiting exoplanet to be discovered from a wide-field ground based search, and with a mass of 0.138 $\pm$ 0.019 M$_J$ it is approximately half-way between the masses of Neptune and Saturn. However HATS-8b has a radius of 0.873 (+0.123,-0.075) R$_J$, resulting in a bulk density of just 0.259 $\pm$ 0.091 g.cm$^{-3}$. The metallicity of the host star is super-Solar ([Fe/H]=0.210 $\pm$ 0.080), arguing against the idea that low density exoplanets form from metal-poor environments. The low density and large radius of HATS-8b results in an atmospheric scale height of almost 1000 km, and in addition to this there is an excellent reference star of near equal magnitude at just 19 arcsecond separation on the sky. These factors make HATS-8b an exciting target for future atmospheric characterization studies, particularly for long-slit transmission spectroscopy.Comment: 11 pages, 7 figures, accepted for publication in A