The range of the tangential Cauchy-Riemann system on a CR embedded manifold

We prove that every compact, pseudoconvex, orientable, CR manifold of \C^n, bounds a complex manifold in the $C^\infty$ sense. In particular, the tangential Cauchy-Riemann system has closed range

Renormalization Group Treatment of Nonrenormalizable Interactions

The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. Explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the na\"ive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms.Comment: LaTex, 11 page

Non-Relativistic Gravitation: From Newton to Einstein and Back

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.Comment: 10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introductio

Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order

The "dialogue of multipoles" matched asymptotic expansion for small black holes in the presence of compact dimensions is extended to the Post-Newtonian order for arbitrary dimensions. Divergences are identified and are regularized through the matching constants, a method valid to all orders and known as Hadamard's partie finie. It is closely related to "subtraction of self-interaction" and shows similarities with the regularization of quantum field theories. The black hole's mass and tension (and the "black hole Archimedes effect") are obtained explicitly at this order, and a Newtonian derivation for the leading term in the tension is demonstrated. Implications for the phase diagram are analyzed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension - a dimension where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio

A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order

The motion of a small compact object in a background spacetime is investigated in the context of a model nonlinear scalar field theory. This model is constructed to have a perturbative structure analogous to the General Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the effective field theory approach to this model and calculate the finite part of the self force on the small compact object through third order in the ratio of the size of the compact object to the curvature scale of the background (e.g., black hole) spacetime. We use well-known renormalization methods and demonstrate the consistency of the formalism in rendering the self force finite at higher orders within a point particle prescription for the small compact object. This nonlinear scalar model should be useful for studying various aspects of higher-order self force effects in EMRIs but within a comparatively simpler context than the full gravitational case. These aspects include developing practical schemes for higher order self force numerical computations, quantifying the effects of transient resonances on EMRI waveforms and accurately modeling the small compact object's motion for precise determinations of the parameters of detected EMRI sources.Comment: 30 pages, 8 figure

CMB Signals of Neutrino Mass Generation

We propose signals in the cosmic microwave background to probe the type and spectrum of neutrino masses. In theories that have spontaneous breaking of approximate lepton flavor symmetries at or below the weak scale, light pseudo-Goldstone bosons recouple to the cosmic neutrinos after nucleosynthesis and affect the acoustic oscillations of the electron-photon fluid during the eV era. Deviations from the Standard Model are predicted for both the total energy density in radiation during this epoch, \Delta N_nu, and for the multipole of the n'th CMB peak at large n, \Delta l_n. The latter signal is difficult to reproduce other than by scattering of the known neutrinos, and is therefore an ideal test of our class of theories. In many models, the large shift, \Delta l_n \approx 8 n_S, depends on the number of neutrino species that scatter via the pseudo-Goldstone boson interaction. This interaction is proportional to the neutrino masses, so that the signal reflects the neutrino spectrum. The prediction for \Delta N_nu is highly model dependent, but can be accurately computed within any given model. It is very sensitive to the number of pseudo-Goldstone bosons, and therefore to the underlying symmetries of the leptons, and is typically in the region of 0.03 < \Delta N_nu < 1. This signal is significantly larger for Majorana neutrinos than for Dirac neutrinos, and, like the scattering signal, varies as the spectrum of neutrinos is changed from hierarchical to inverse hierarchical to degenerate.Comment: 40 pages, 4 figure

The k-Point Random Matrix Kernels Obtained from One-Point Supermatrix Models

The k-point correlation functions of the Gaussian Random Matrix Ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials

Observations of Rapid Disk-Jet Interaction in the Microquasar GRS 1915+105

We present evidence that ~ 30 minute episodes of jet formation in the Galactic microquasar GRS 1915+105 may sometimes entirely be a superposition of smaller, faster phenomena. We base this conclusion on simultaneous X-ray and infrared observations in July 2002, using the Rossi X-ray Timing Explorer and the Palomar 5 meter telescope. On two nights, we observed quasi-periodic infrared flares from GRS 1915+105, each accompanied by a set of fast oscillations in the X-ray light curve (indicating an interaction between the jet and accretion disk). In contrast to similar observations in 1997, we find that the duration of each X-ray cycle matches the duration of its accompanying infrared flare, and we observed one instance in which an isolated X-ray oscillation occurred at the same time as a faint infrared "subflare" (of duration ~ 150 seconds) superimposed on one of the main flares. From these data, we are able to conclude that each X-ray oscillation had an associated faint infrared flare and that these flares blend together to form, and entirely comprise, the ~ 30 minute events we observed. Part of the infrared emission in 1997 also appears to be due to superimposed small flares, but it was overshadowed by infrared-bright ejections associated with the appearance of a sharp "trigger" spike in each X-ray cycle that were not present in 2002. We also study the evolution of the X-ray spectrum and find significant differences in the high energy power law component, which was strongly variable in 1997 but not in 2002. Taken together, these observations reveal the diversity of ways in which the accretion disk and jet in black hole systems are capable of interacting and solidify the importance of the trigger spike for large ejections to occur on ~ 30 minute timescales in GRS 1915+105.Comment: 17 pages, 9 figures; accepted for publication in The Astrophysical Journa

Does Low Frequency X-ray QPO Behavior in GRS 1915+105 Influence Subsequent X-ray and Infrared Evolution?

Using observations with the Rossi X-ray Timing Explorer, we examine the behavior of 2-10 Hz quasi-periodic oscillations (QPOs) during spectrally-hard dips in the x-ray light curve of GRS 1915+105 that are accompanied by infrared flares. Of the twelve light-curves examined, nine are beta-class and three are alpha-class following the scheme of Belloni et al. (2000). In most cases, the QPO frequency is most strongly correlated to the power law flux, which partially contradicts some earlier claims that the strongest correlation is between QPO frequency and blackbody flux. Seven beta-class curves are highly correlated to blackbody features. In several cases, the QPO evolution appears to decouple from the spectral evolution. We find that beta-class light-curves with strong correlations can be distinguished from those without by their ``trigger spike'' morphology. We also show that the origin and strength of the subsequent infrared flare may be causally linked to the variations in QPO frequency evolution and not solely tied to the onset of soft x-ray flaring behavior. We divide the twelve alpha- and beta-class light-curves into three groups based on the evolution of the QPO, the morphology of the trigger spike, and the infrared flare strength. An apparent crossover case leads us to conclude that these groups are not unique modes but represent part of a continuum of accretion behaviors. We believe the QPO behavior at the initiation of the hard dip can ultimately be used to determine the terminating x-ray behavior, and the following infrared flaring behavior.Comment: 29 pages, 9 figures, to be published in Ap