Amoebas and Instantons

We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills on $\mathbb{R}^4\times S^1$ and as K\"ahler gravity on local SU(N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model. The limit shape is linked with a hyperelliptic curve, which is a five-dimensional version of the SU(N) Seiberg-Witten curve. Amoebas and the Ronkin functions play intermediary roles between the limit shape and the hyperelliptic curve. In particular, the Ronkin function realizes an integration of thermodynamical density of the main diagonal partitions, along one-dimensional slice of it and thereby is interpreted as the counting function of gauge instantons. The radius of $S^1$ can be identified with the inverse temperature of the statistical model. The large radius limit of the five-dimensional Yang-Mills is the low temperature limit of the statistical model, where the statistical model is frozen to a ground state that is associated with the local SU(N) geometry. We also show that the low temperature limit corresponds to a certain degeneration of amoebas and the Ronkin functions known as tropical geometry.Comment: 58 pages, 28 figures, references adde

Constraining Physical Properties of Type IIn Supernovae through Rise Times and Peak Luminosities

We investigate the diversity in the wind density, supernova ejecta energy, and ejecta mass in Type IIn supernovae based on their rise times and peak luminosities. We show that the wind density and supernova ejecta properties can be estimated independently if both the rise time and peak luminosity are observed. The peak luminosity is mostly determined by the supernova properties and the rise time can be used to estimate the wind density. We find that the ejecta energy of Type IIn supernovae needs to vary by factors of 0.2-5 from the average if their ejecta mass is similar. The diversity in the observed rise times indicates that their wind density varies by factors of 0.2-2 from the average. We show that Type IIn superluminous supernovae should have not only large wind density but also large ejecta energy and/or small ejecta mass to explain their large luminosities and the rise times at the same time. We also note that the shock breakout does not necessarily occur in the wind even if it is optically thick, except for the case of superluminous supernovae, and we analyze the observational data both with and without assuming that the shock breakout occurs in the dense wind of Type IIn supernovae.Comment: 6 pages, 2 figures, 2 tables, accepted by The Astrophysical Journal Letter

Covariant Gravitational Equations on Brane World with Gauss-Bonnet term

We present the covariant gravitational equations to describe a four-dimensional brane world in the case with the Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the $Z_2$ symmetric brane. It contains some components of five-dimensional Weyl curvature ($E_{\mu\nu}$) which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.Comment: 14 pages, no figur

Circumstellar and explosion properties of Type Ibn supernovae

We investigate circumstellar and explosion properties of Type Ibn supernovae (SNe) by analyzing their bolometric light curves. Bolometric light curves of Type Ibn SNe generally have a large contrast between peak luminosity and late-phase luminosity, which is much larger than those of 56Ni-powered SNe. Thus, most of them are likely powered by the interaction between SN ejecta and dense circumstellar media. In addition, Type Ibn SNe decline much faster than Type IIn SNe, and this indicates that the interaction in Type Ibn SNe ceases earlier than in Type IIn SNe. Thus, we argue that Type Ibn SN progenitors experience high mass-loss rates in a short period just before explosion, while Type IIn SN progenitors have high mass-loss rates sustained for a long time. Furthermore, we show that rise time and peak luminosity of Type Ibn and Type IIn SNe are similar and thus, they have similar explosion properties and circumstellar density. The similar circumstellar density in the two kinds of SNe may indicate that mass-loss rates of Type Ibn SN progenitors are generally higher than those of Type IIn as the wind velocities inferred from narrow spectral components are generally higher in Type Ibn SNe. We also show that 56Ni mass and explosion energy of Type Ibn SNe may be smaller than those of other stripped-envelope SNe, probably because they tend to suffer large fallback or some of them may not even be terminal stellar explosions.Comment: 7 pages, 4 figures, 1 table, accepted by The Astrophysical Journa

Extracting information behind the veil of horizon

In AdS/CFT duality, it is often argued that information behind the event horizon is encoded even in boundary correlators. However, its implication is not fully understood. We study a simple model which can be analyzed explicitly. The model is a two-dimensional scalar field propagating on the s-wave sector of the BTZ black hole formed by the gravitational collapse of a null dust. Inside the event horizon, we placed an artificial timelike singularity where one-parameter family of boundary conditions is permitted. We compute two-point correlators with two operators inserted on the boundary to see if the parameter is reflected in the correlators. In a typical case, we give an explicit form of the boundary correlators of an initial vacuum state and show that the parameter can be read off from them. This does not immediately imply that the asymptotic observer can extract the information of the singularity since one cannot control the initial state in general. Thus, we also study whether the parameter can be read off from the correlators for a class of initial states.Comment: 17pages, 5 figures, accepted in Physical Review

Multi-band polarization of Type IIP supernovae due to light echo from circumstellar dust

Type IIP supernovae (SNe IIP) often show relatively high continuum polarization ($\sim 1$\%) in the late phase. This polarization feature is generally believed to be due to an inner aspherical core revealed in the late phase, while this polarization feature can also be contributed by the effect of polarized-scattered echoes by circumstellar (CS) dust around the SN. In this paper, we propose a unique method to distinguish polarization from the SN ejecta and from the light echo. We quantitatively examine wavelength dependence of the polarization created by the scattered echoes for various geometries and amounts of CS dust. It is found that the polarization in the $U$-band has characteristic features, i.e., the polarization emerges at an earlier phase with higher polarization degree than that in longer wavelengths. These are due to the rapid evolution of the $U$-band light curve as well as higher optical depth of dust in shorter wavelengths. Except for the $U$ band, the polarization increases after the plateau phase, and the polarization degree is generally higher for shorter wavelengths. These polarimetric features can be easily distinguished from the polarization expected from an aspherical core, which predicts almost no wavelength dependence. Moreover, we show that multi-band polarimetric observations for SNe IIP can constrain a parameter space in the CS dust mass and distance from the SNe. We thus encourage multi-band polarimetric observations for SNe IIP.Comment: 12 pages, 15 figures, accepted for publication in the Astrophysical Journa

Circumstellar Light Echo as a Possible Origin of the Polarization of Type IIP Supernovae

Type IIP supernovae (SNe IIP) are the most common class of core-collapse SNe. They often show rapid increase of polarization degree in the late phase. This time evolution is generally believed to originate from the emergence of an inner aspherical core, while an effect of polarized-scattered echoes by circumstellar (CS) dust around the SN may also substantially contribute to this polarization feature. In this study, we examine the effects of the scatted echoes on the SN polarization through radiative transfer simulations for various geometry and amount of CS dust. It has been found that asymmetrically-distributed CS dust, which is generally inferred for red supergiants, could reproduce the observed polarization features. We have applied our results to SNe 2004dj and 2006ov, deriving the geometry and amount of CS dust to explain their observed polarization features in this scenario. For both SNe, the blob-like or bipolar distribution of CS dust rather than the disk-like distribution is favored. The derived dust mass $M_{\mathrm{dust}}$ in the blob model (the bipolar CS dust model) for SNe 2004dj and 2006ov are $\sim 7.5 \times 10^{-4}$ M$_{\odot}$ ($\sim 8.5 \times10^{-4}$ M$_{\odot}$) and $\sim 5.2 \times 10^{-4}$ M$_{\odot}$ ($\sim 1.3 \times10^{-3}$ M$_{\odot}$), respectively. Even in the case where this process would not play a dominant role in the observed polarization signals, this effect should in principle contribute to it, the strength of which depends on the nature of CS dust. Therefore, this effect must be taken into account in discussing multi-dimensional structure of an SN explosion through polarimetric observations.Comment: Accepted for publication in ApJ. 13 pages, 17 figure

Quasinormal modes for nonextreme Dp-branes and thermalizations of super-Yang-Mills theories

The nonextreme Dp-brane solutions in type II supergravity(in the near-horizon limit) are expected to be dual to (p+1)-dimensional noncompact supersymmetric Yang-Mills theories at finite temperature. We study the translationally invariant perturbations along the branes in those backgrounds and calculate quasinormal frequencies numerically. These frequencies should determine the thermalization time scales in the dual Yang-Mills theories.Comment: 13 pages, 3 figures, revtex4; v2 & 3: references added, minor change

Asymptotic singular behavior of Gowdy spacetimes in string theory

We study $T^{3}$ Gowdy spacetimes in the Einstein-Maxwell-dilaton-axion system and show by the Fuchsian algorithm that they have in general asymptotically velocity-term dominated singularities. The families of the corresponding solutions depend on the maximum number of arbitrary functions. Although coupling of the dilaton field with the Maxwell and/or the axion fields corresponds to the ``potential'' which appears in the Hamiltonian of vacuum Bianchi IX spacetimes, our result means that the spacetimes do not become Mixmaster necessarily.Comment: 13 pages, submitted to Class. Quantum Gra

Polarization as a probe of dusty environments around Type Ia supernovae: radiative transfer models for SN 2012dn

Geometry of circumstellar (CS) medium around supernovae (SNe) provides important diagnostics to understand the nature of their progenitors. In this paper, properties of CS dust around SN 2012dn, a super-Chandrasekhar candidate Type Ia supernova (SC-SN), have been studied through detailed three dimensional radiation transfer simulations. With the detected near-infrared excess from SN 2012dn, we show that it has a disk-like dusty CS environment whose mass is roughly consistent with a branch of an accreting white dwarf system (the single degenerate scenario). We show that a similar system should produce polarization signals up to $\sim 8$ \% in the $B$ band, depending on the viewing direction if polarimetric observation is performed. We predict that the maximum polarization is reached around $\sim 60$ days after the $B$-band maximum. We show that the temporal and wavelength dependence of the polarization signals, together with other unique features, can be easily distinguished from the interstellar polarization and intrinsic SN polarization. Indeed, the small polarization degree observed for normal Type Ia SNe (SNe Ia) can constrain a parameter space in the CS dust mass and distribution. We thus encourage multi-band polarimetric observations for SNe Ia, especially for outliers including SC-SNe for which some arguments for the single degenerate scenario exist but the polarization data are very rare so far.Comment: 9 pages, 7 figures, 2 tables, accepted for publication by MNRA