Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic

Is N = 8 Supergravity Ultraviolet Finite?

Conventional wisdom holds that no four-dimensional gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. Recent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the so-called `no-triangle hypothesis', which states that triangle and bubble integrals cancel from these amplitudes. A consequence of this hypothesis is that for any number of external legs, at one loop N = 8 supergravity and N = 4 super-Yang-Mills have identical superficial degrees of ultraviolet behavior in D dimensions. We describe how the unitarity method allows us to promote these one-loop cancellations to higher loops, suggesting that previous power counts were too conservative. We discuss higher-loop evidence suggesting that N = 8 supergravity has the same degree of divergence as N = 4 super-Yang-Mills theory and is ultraviolet finite in four dimensions. We comment on calculations needed to reinforce this proposal, which are feasible using the unitarity method.Comment: 7 pages, 5 figures, revte

Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms

We demonstrate a scheme, based on a cascade of lithium niobate intensity and phase modulators driven by specially tailored radio frequency waveforms to generate an optical frequency comb with very high spectral flatness. In this work we demonstrate a 10 GHz comb with ~40 lines with spectral power variation below 1-dB and ~60 lines in total. The number of lines that can be generated is limited by the power handling capability of the phase modulator, and this can be scaled without compromising the spectral flatness. Furthermore, the spectral phase of the generated combs in our scheme is almost purely quadratic which, as we will demonstrate, allows for very high quality pulse compression using only single mode fiber.Comment: 12 pages, 3 figures, replaced the older version with the published versio

The D^{2k} R^4 Invariants of N=8 Supergravity

The existence of a linearized SUSY invariant for N=8 supergravity whose gravitational components are usually called R^4 was established long ago by on-shell superspace arguments. Superspace and string theory methods have also established analogous higher dimensional D^{2k} R^4 invariants. However, very little is known about the SUSY completions of these operators which involve other fields of the theory. In this paper we find the detailed component expansion of the linearized R^4 invariant starting from the corresponding superamplitude which generates all component matrix elements of the operator. It is then quite straightforward to extend results to the entire set of D^{2k} R^4 operators.Comment: 17 page

Transit confirmation and improved stellar and planet parameters for the super-Earth HD 97658 b and its host star

Super-Earths transiting nearby bright stars are key objects that simultaneously allow for accurate measurements of both their mass and radius, providing essential constraints on their internal composition. We present here the confirmation, based on Spitzer transit observations, that the super-Earth HD 97658 b transits its host star. HD 97658 is a low-mass ($M_*=0.77\pm0.05\,M_{\odot}$) K1 dwarf, as determined from the Hipparcos parallax and stellar evolution modeling. To constrain the planet parameters, we carry out Bayesian global analyses of Keck-HIRES radial velocities, and MOST and Spitzer photometry. HD 97658 b is a massive ($M_P=7.55^{+0.83}_{-0.79} M_{\oplus}$) and large ($R_{P} = 2.247^{+0.098}_{-0.095} R_{\oplus}$ at 4.5 $\mu$m) super-Earth. We investigate the possible internal compositions for HD 97658 b. Our results indicate a large rocky component, by at least 60% by mass, and very little H-He components, at most 2% by mass. We also discuss how future asteroseismic observations can improve the knowledge of the HD 97658 system, in particular by constraining its age. Orbiting a bright host star, HD 97658 b will be a key target for coming space missions TESS, CHEOPS, PLATO, and also JWST, to characterize thoroughly its structure and atmosphere.Comment: 8 figures, accepted to Ap

Effects of clumping on temperature I: externally heated clouds

We present a study of radiative transfer in dusty, clumpy star-forming regions. A series of self-consistent, 3-D, continuum radiative transfer models are constructed for a grid of models parameterized by central luminosity, filling factor, clump radius, and face-averaged optical depth. The temperature distribution within the clouds is studied as a function of this parameterization. Among our results, we find that: (a) the effective optical depth is smaller in clumpy regions than in equivalent homogeneous regions; (b) penetration of radiation is drive by the fraction of open sky (FOS) -- which measures the fraction of solid angle which is devoid of clumps; (c) FOS increases as clump radius increases and filling factor decreases; (d) for FOS > 0.6-0.8 the sky is sufficiently open that the temperature is relatively insensitive to FOS; (e) the physical process by which radiation penetrates is streaming between clumps; (f) filling factor dominates the temperature distribution for large optical depths, and at small clump radii for small optical depths; (g) at lower optical depths, the temperature distribution is most sensitive to filling factors of 1-10 per cent, in accordance with many observations; (h) direct shadowing can be important approximately one clump radius behind a clump.Comment: 12 pages, 17 figures, accepted by MNRA

Can we detect local helioseismic parameter shifts in coronal holes?

Changes in helioseismic mode parameters in active regions and across the solar disk are well documented, but local magnetic activity and geometric effects may not account for all of the scatter seen in the results. We use results from theHelioseismic and Magnetic Imagerring-diagram pipeline for Carrington rotation 2113 to look for differences in mode amplitude and frequency between coronal holes and other quiet-Sun regions. While we do not find a systematic difference, the results do suggest that the correlation between magnetic activity index and mode parameters shows less scatter in coronal hole regions than in general quiet Sun

An action for the (2,0) self-dual tensor multiplet in a conformal supergravity background

We present the action for a self-dual tensor in six dimensions, coupled to a (2,0) conformal supergravity background. This action gives rise to the expected equations of motion. An alternative look upon one of the gauge symmetries clarifies its role in the supersymmetry transformation rules and the realisation of the algebra.Comment: 14 pages, accepted by Class. Quant. Gra