Exploring Vacuum Structure around Identity-Based Solutions

We explore the vacuum structure in bosonic open string field theory expanded around an identity-based solution parameterized by $a(>=-1/2)$. Analyzing the expanded theory using level truncation approximation up to level 20, we find that the theory has the tachyon vacuum solution for $a>-1/2$. We also find that, at $a=-1/2$, there exists an unstable vacuum solution in the expanded theory and the solution is expected to be the perturbative open string vacuum. These results reasonably support the expectation that the identity-based solution is a trivial pure gauge configuration for $a>-1/2$, but it can be regarded as the tachyon vacuum solution at $a=-1/2$.Comment: 12 pages, 5 figures; new numerical data up to level (20,60) included; Contribution to the proceedings of "Second International Conference on String Field Theory and Related Aspects" (Steklov Mathematical Institute, Moscow, Russia, April 12-19, 2009

Open String Field Theory around Universal Solutions

We study the physical spectrum of cubic open string field theory around universal solutions, which are constructed using the matter Virasoro operators and the ghost and anti-ghost fields. We find the cohomology of the new BRS charge around the solutions, which appear with a ghost number that differs from that of the original theory. Considering the gauge-unfixed string field theory, we conclude that open string excitations perturbatively disappear after the condensation of the string field to the solutions.Comment: 14 pages, LaTeX with ptptex.cls, typos correcte

Regularization of identity based solution in string field theory

We demonstrate that an Erler-Schnabl type solution in cubic string field theory can be naturally interpreted as a gauge invariant regularization of an identity based solution. We consider a solution which interpolates between an identity based solution and ordinary Erler-Schnabl one. Two gauge invariant quantities, the classical action and the closed string tadpole, are evaluated for finite value of the gauge parameter. It is explicitly checked that both of them are independent of the gauge parameter.Comment: 9 pages, minor typos corrected and references adde

Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test

Quantum Coherence of Relic Neutrinos

We argue that in at least a portion of the history of the universe the relic background neutrinos are spatially-extended, coherent superpositions of mass states. We show that an appropriate quantum mechanical treatment affects the neutrino mass values derived from cosmological data. The coherence scale of these neutrino flavor wavepackets can be an appreciable fraction of the causal horizon size, raising the possibility of spacetime curvature-induced decoherence.Comment: 4 pages, 4 figures; matches publication in PR

The Location of the Nucleus of NGC 1068 and the Three-dimensional Structure of Its Nuclear Region

The HST archival UV imaging polarimetry data of NGC 1068 is re-examined. Through an extensive estimation of the observational errors, we discuss whether the distribution of the position angles (PAs) of polarization is simply centrosymmetric or not. Taking into account the effect of a bad focus at the time of the observation, we conclude that, within the accuracy of HST/FOC polarimetry, the PA distribution is completely centrosymmetric. This means that the UV polarization originates only from scattering of the radiation from a central point-like source. However, our analysis shows that the most probable location of the nucleus is only ~0.''08 (~6pc) south from the brightest cloud called ``cloud B''. The error circle of 99% confidence level extends to cloud B and to ``cloud A'' which is about 0.''2 south of cloud B. By this FOC observation, Cloud B is only marginally rejected as the nucleus. Assuming that the UV flux is dominated by electron-scattered light, we have also derived a three-dimensional structure of the nuclear region. The inferred distribution suggests a linear structure which could be related to the radio jet.Comment: 19 pages, 14 figures, to be published in the Astrophysical Journa

Neutrino Burst-Generated Gravitational Radiation From Collapsing Supermassive Stars

We estimate the gravitational radiation signature of the electron/positron annihilation-driven neutrino burst accompanying the asymmetric collapse of an initially hydrostatic, radiation-dominated supermassive object suffering the Feynman-Chandrasekhar instability. An object with a mass $5\times10^4\,M_\odot<M<5\times10^5\,M_\odot$, with primordial metallicity, is an optimal case with respect to the fraction of its rest mass emitted in neutrinos as it collapses to a black hole: lower initial mass objects will be subject to scattering-induced neutrino trapping and consequently lower efficiency in this mode of gravitational radiation generation; while higher masses will not get hot enough to radiate significant neutrino energy before producing a black hole. The optimal case collapse will radiate several percent of the star's rest mass in neutrinos and, with an assumed small asymmetry in temperature at peak neutrino production, produces a characteristic linear memory gravitational wave burst signature. The timescale for this signature, depending on redshift, is $\sim1{\rm~s}$ to $10{\rm~s}$, optimal for proposed gravitational wave observatories like DECIGO. Using the response of that detector, and requiring a signal-to-noise ratio SNR $>$ 5, we estimate that collapse of a $\sim 5\times10^4\,M_\odot$ supermassive star could produce a neutrino burst-generated gravitational radiation signature detectable to redshift $z\lesssim7$. With the envisioned ultimate DECIGO design sensitivity, we estimate that the linear memory signal from these events could be detectable with SNR $> 5$ to $z \lesssim13$.Comment: 15 pages, 8 figure