arXiv subjects
Publications and source records attributed to Hiroaki Nakajima.
We study a family of the non-vacuum stationary axisymmetric type D metrics, where the two principal null directions are geodesic and shearfree. It is demonstrated that the conformal-to-Carter metric gives the most general form of this family, without any assumptions which are previously used by Ovcharenko and Podolský to arrive at this conclusion.
The gravitational form factors (GFFs) of the baryon octet, including hyperons, are investigated in a bottom-up holographic QCD model that explicitly incorporates the SU(3) flavor symmetry breaking through the strange quark mass. We fit the model parameters to reproduce the empirical masses of the baryon octet and examine the dependence of GFFs on the probe momentum. Our numerical results show distinct differences in the GFFs across the baryon octet. The computed GFFs are found to be in reasonable agreement with available lattice QCD results for the non-strange/nucleon sector. We also calculate the gravitational radii of the baryon octet and find that they decrease with increasing strangeness, indicating that heavier hyperons are more compact.
We study the wave equations with the various spins on the background of the Kerr metric deformed by a function of the radial coordinate, on which background we have studied the gravitational-wave equations previously. We obtain the unified expression of the Teukolsky-like master equations and the corresponding radial equations with various spins. We find that taking the separable gauge introduced in previous study simplifies the unified form. We also discuss the structure of the radial equation as an ordinary differential equation, such as the existence of the regular and the irregular singularities of the equation and the behavior of the solution around each singularity.
We study an axisymmetric metric satisfying the Petrov type D property with some additional ansatze, but without assuming the vacuum condition. We find that our metric in turn becomes conformal to the Kerr metric deformed by one function of the radial coordinate. We then study the gravitational-wave equations on this background metric in the case that the conformal factor is unity. We find that under an appropriate gauge condition, the homogeneous wave equations admit the separation of the variables, which is also helpful for solving the nonhomogeneous equations. The resultant ordinary differential equation for the radial coordinate gives a natural extension of the Teukolsky equation.
We study the wave equations with various spins on the background of the general spherically symmetric spacetime. We obtain the unified expression of the Teukolsky-like master equations and the corresponding radial equations with the general spins. We also discuss the gauge dependence in the gravitational-wave equations, which have appeared in the previous studies.
We construct the gravitational-wave equation in the background of the effective one-body system for the spinless binary, which is in general available with the spherically symmetric background as well. The gauge conditions are given in terms of the metric perturbation.
We construct a new type of Chandrasekhar transformation in Kerr spacetime using the different tortoise coordinate, which is useful for exact analysis to study Teukolsky equation with arbitrary frequency. We also give the interpretation of our transformation using the formalism of the quantum Seiberg-Witten geometry.
Independent low-rank matrix analysis (ILRMA) is a fast and stable method for blind audio source separation. Conventional ILRMAs assume time-variant (super-)Gaussian source models, which can only represent signals that follow a super-Gaussian distribution. In this paper, we focus on ILRMA based on a generalized Gaussian distribution (GGD-ILRMA) and propose a new type of GGD-ILRMA that adopts a time-variant sub-Gaussian distribution for the source model. By using a new update scheme called generalized iterative projection for homogeneous source models, we obtain a convergence-guaranteed update rule for demixing spatial parameters. In the experimental evaluation, we show the versatility of the proposed method, i.e., the proposed time-variant sub-Gaussian source model can be applied to various types of source signal.
Recently, deep neural network (DNN) has made a breakthrough in monaural source enhancement. Through a training step by using a large amount of data, DNN estimates a mapping between mixed signals and clean signals. At this time, we use an objective function that numerically expresses the quality of a mapping by DNN. In the conventional methods, L1 norm, L2 norm, and Itakura-Saito divergence are often used as objective functions. Recently, an objective function based on short-time objective intelligibility (STOI) has also been proposed. However, these functions only indicate similarity between the clean signal and the estimated signal by DNN. In other words, they do not show the quality of noise reduction or source enhancement. Motivated by the fact, this paper adopts signal-to-distortion ratio (SDR) as the objective function. Since SDR virtually shows signal-to-noise ratio (SNR), maximizing SDR solves the above problem. The experimental results revealed that the proposed method achieved better performance than the conventional methods.
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
We study the twisted N=4 super Yang-Mills theories in the Omega-background with the constant R-symmetry Wilson line gauge field. Based on the classification of topological twists of N=4 supersymmetry (the half, the Vafa-Witten and the Marcus twists), we construct the deformed off-shell supersymmetry associated with the scalar supercharges for these twists. We find that the Omega-deformed action is written in the exact form with respect to the scalar supercharges as in the undeformed case.
We study the dimensional reduction of ten-dimensional super Yang-Mills theory in curved backgrounds with torsion. We examine the parallel spinor conditions and the constraints for the torsion parameters which preserve supersymmetry and gauge symmetry in four dimensions. In particular we examine the ten-dimensional Omega-background with the torsion which is identified with the R-symmetry Wilson line gauge fields. After the dimensional reduction, we obtain the Omega-deformed N=4 super Yang-Mills theory. Solving the parallel spinor conditions and the torsion constraints, we classify the deformed supersymmetry associated with the topological twist of N=4 supersymmetry. We also study deformed supersymmetries in the Nekrasov-Shatashvili limit.
We investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. We systematically classify the BPS equations in terms of the number of supersymmetry and the R-symmetries of the undeformed and mass-deformed ABJM theories. For the undeformed case, we analyze the ${\cal N}=2$ BPS equations for U(2)$\times$U(2) gauge symmetry and obtain a coupled differential equation which can be reduced to either Liouville- or Sinh-Gordon-type vortex equations according to the choice of scalar functions. For the mass-deformed case with U($N$)$\times$U($N$) gauge symmetry, we obtain some number of pairs of coupled differential equations from the ${\cal N}=1,2$ BPS equations, which can be reduced to the vortex equations in Maxwell-Higgs theory or Chern-Simons matter theories as special cases. We discuss the solutions. In ${\cal N}=3$ vortex equations Chern-Simons-type vortex equation is not allowed. We also show that ${\cal N}=\frac52, \frac32, \frac12$ BPS equations are equivalent to those with higher integer supersymmetries.
We consider the open superstring action in AdS_5 x S^5 background with the bilinear Wess-Zumino term, which has been modified in such a way that a certain total derivative term is absent, and give the covariant description of supersymmetric D-branes. We show that the modification of bilinear Wess-Zumino term is necessary to describe correctly the 1/2-BPS D(-1)-brane in AdS_5 x S^5 background, while the classification of other supersymmetric D-branes does not depend on such modification.
We study the instanton calculus for N=4 super Yang-Mills theory in ten-dimensional Omega-background with the R-symmetry Wilson line gauge field. From the ADHM construction of instantons in the background, we obtain the deformed instanton effective action. For a certain case we get the effective action of N=2^* theory in the Omega-background. We also study the low-energy effective D(-1)-brane action for the D3/D(-1)-brane system in the R-R 3-form field strength backgrounds and find that the action agrees with the instanton effective action in the Omega-background.
In this paper we investigate the relationship between the so-called fermionic T-duality and the Morita equivalence of noncommutative supertori. We first get an action satisfying the BRST invariance under nonvanishing constant R-R and NS-NS backgrounds in the hybrid formalism. We investigate the effect of bosonic T-duality transformation together with fermionic T-duality transformation in this background and look for the resultant symmetry of transformations. We find that the duality transformations correspond to Morita equivalence of noncommutative supertori. In particular, we obtain the symmetry group $SO(2,2,{\cal V}_{\Z}^0)$ in two dimensions, where ${\cal V}_{\Z}^0$ denotes Grassmann even number whose body part belongs to ${\Z}$.
We study the relation between the ADHM construction of instantons in the Omega-background and the fractional D3/D(-1)-branes at the orbifold singularity of C \times C^2/Z_2 in Ramond-Ramond (R-R) 3-form field strength background. We calculate disk amplitudes of open strings connecting the D3/D(-1)-branes in certain R-R background to obtain the D(-1)-brane effective action deformed by the R-R background. We show that the deformed D(-1)-brane effective action agrees with the instanton effective action in the Omega-background.
In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts. Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group $SO(2,2,V_{\Z}^0)$, where $V_{\Z}^0$ denotes Grassmann even number whose body part belongs to ${\Z}$, yields Morita equivalent noncommutative supertori in two dimensions.