arXiv subjects

Yasuhiro Abe

Publications and source records attributed to Yasuhiro Abe.

At least 19 recordsLinked to original sources

arXiv2020

Current status and future plan of Osaka Prefecture University 1.85-m mm-submm telescope project

We report the current status of the 1.85-m mm-submm telescope installed at the Nobeyama Radio Observatory (altitude 1400 m) and the future plan. The scientific goal is to reveal the physical/chemical properties of molecular clouds in the Galaxy by obtaining large-scale distributions of molecular gas with an angular resolution of several arcminutes. A semi-automatic observation system created mainly in Python on Linux-PCs enables effective operations. A large-scale CO $J=$2--1 survey of the molecular clouds (e.g., Orion-A/B, Cygnus-X/OB7, Taurus-California-Perseus complex, and Galactic Plane), and a pilot survey of emission lines from minor molecular species toward Orion clouds have been conducted so far. The telescope also is providing the opportunities for technical demonstrations of new devices and ideas. For example, the practical realizations of PLM (Path Length Modulator) and waveguide-based sideband separating filter, installation of the newly designed waveguide-based circular polarizer and OMT (Orthomode Transducer), and so on. As the next step, we are now planning to relocate the telescope to San Pedro de Atacama in Chile (altitude 2500 m), and are developing very wideband receiver covering 210--375 GHz (corresponding to Bands 6--7 of ALMA) and full-automatic observation system. The new telescope system will provide large-scale data in the spatial and frequency domain of molecular clouds of Galactic plane and Large/Small Magellanic Clouds at the southern hemisphere. The data will be precious for the comparison with those of extra-galactic ones that will be obtained with ALMA as the Bands 6/7 are the most efficient frequency bands for the surveys in extra-galaxies for ALMA.

astro-ph.IM↗

arXiv2020

Large Thermoelectric Power Factor in Whisker Crystals of Solid Solutions of the One-Dimensional Tellurides Ta4SiTe4 and Nb4SiTe4

One-dimensional tellurides Ta4SiTe4 and Nb4SiTe4 were found to show high thermoelectric performance below room temperature. This study reported the synthesis and thermoelectric properties of whisker crystals of Ta4SiTe4-Nb4SiTe4 solid solutions and Mo- or Ti-doped (Ta0.5Nb0.5)4SiTe4. Thermoelectric power of the solid solutions systematically increased with increasing Ta content, while their electrical resistivity was unexpectedly small. Mo- and Ti-doped (Ta0.5Nb0.5)4SiTe4 showed n- and p-type thermoelectric properties with large power factors exceeding 40 microW cm-1 K-2, respectively. The fact that not only Ta4SiTe4 and Nb4SiTe4 but also their solid solutions showed high performance indicated that this system is a promising candidate for thermoelectric applications at low temperatures.

cond-mat.mtrl-sci↗

arXiv2019

Some properties of zero-mode wave functions in abelian Chern-Simons theory on the torus

In geometric quantization a zero-mode wave function in abelian Chern-Simons theory on the torus can be defined as $Ψ[ a, \bar{a} ] = e^{- \frac{K(a, \bar{a})}{2}} f (a)$ where $K(a ,\bar{a} )$ denotes a Kähler potential for the zero-mode variable $a \in \mathbb{C}$ on the torus. We first review that the holomorphic wave function $f(a)$ can be described in terms of the Jacobi theta functions by imposing gauge invariance on $Ψ[ a, \bar{a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. We discuss that $f(a)$ is quantum theoretically characterized by ($i$) an operative relation in the $a$-space representation and ($ii$) an inner product of $Ψ[ a, \bar{a} ]$'s including ambiguities in the choice of $K(a ,\bar{a} )$. We then carry out a similar analysis on the gauge invariance of $Ψ[ a , \bar{a} ]$ where the gauge transformations are induced by modular transformations of the zero-mode variable. We observe that$f(a)$ behaves as a modular form of weight 2 under the condition of $|a|^2 = 1$, namely, $\left. f \left( - \frac{1}{a} \right) = a^2 f(a) \right|_{|a|^2 = 1}$. Utilizing specific forms of $f(a)$ in terms of the Jacobi theta functions, we further investigate how exactly $f(a)$ can or cannot be interpreted as the modular form of weight 2; we extract conditions that make such an interpretation possible.

hep-th↗

arXiv2018

Elements of Aomoto's generalized hypergeometric functions and a novel perspective on Gauss' hypergeometric differential equation

We review Aomoto's generalized hypergeometric functions on Grassmannian spaces Gr(k +1, n+1). Particularly, we clarify integral representations of the generalized hypergeometric functions in terms of twisted homology and cohomology. With an example of the Gr(2, 4) case, we consider in detail Gauss' original hypergeometric functions in Aomoto's framework. This leads us to present a new systematic description of Gauss' hypergeometric differential equation in a form of a first order Fuchsian differential equation.

math.AP↗

arXiv2018

Abelian Chern-Simons theory on the torus and physical views on the Hecke operators

In the previous paper arXiv:1711.07122, we show that a holomorphic zero-mode wave function in abelian Chern-Simons theory on the torus can be considered as a quantum version of a modular form of weight 2. Motivated by this result, in this paper we consider an action of a Hecke operator on such a wave function from a gauge theoretic perspective. This leads us to obtain some physical views on the Hecke operators in number theory.

hep-th↗

arXiv2016

A note on generalized hypergeometric functions, KZ solutions, and gluon amplitudes

Some aspects of Aomoto's generalized hypergeometric functions on Grassmannian spaces $Gr(k+1,n+1)$ are reviewed. Particularly, their integral representations in terms of twisted homology and cohomology are clarified with an example of the $Gr(2,4)$ case which corresponds to Gauss' hypergeometric functions. The cases of $Gr(2, n+1)$ in general lead to $(n+1)$-point solutions of the Knizhnik-Zamolodchikov (KZ) equation. We further analyze the Schechtman-Varchenko integral representations of the KZ solutions in relation to the $Gr(k+1, n+1)$ cases. We show that holonomy operators of the so-called KZ connections can be interpreted as hypergeometric-type integrals. This result leads to an improved description of a recently proposed holonomy formalism for gluon amplitudes. We also present a (co)homology interpretation of Grassmannian formulations for scattering amplitudes in ${\cal N} = 4$ super Yang-Mills theory.

hep-th↗

arXiv2014

Holonomies of gauge fields in twistor space 6: incorporation of massive fermions

Following the previous paper arXiv:1205.4827, we formulate an S-matrix functional for massive fermion ultra-helicity-violating (UHV) amplitudes, i.e., scattering amplitudes of positive-helicity gluons and a pair of massive fermions. The S-matrix functional realizes a massive extension of the Cachazo-Svrcek-Witten (CSW) rules in a functional language. Mass-dimension analysis implies that interactions among gluons and massive fermions should be decomposed into three-point massive fermion subamplitudes. Namely, such interactions are represented by combinations of three-point UHV and next-to-UHV (NUHV) vertices. This feature is qualitatively different from the massive scalar amplitudes where the number of involving gluons can be arbitrary.

hep-th↗

arXiv2013

Holonomies of gauge fields in twistor space 7: an electroweak model

We consider massive deformation of $U(2)$ gauge bosons in a recently developed holonomy formalism and propose a novel electroweak model. The massive gauge bosons arise from massive deformation of spinor momenta, which implies that the mass generation is implemented by Lorentz symmetry breaking rather than the spontaneous gauge symmetry breaking. Following the notation of the holonomy formalism, we interpret the weak hypercharge of a left-handed fermion doublet as the reciprocal of the Knizhnik-Zamolodchikov (KZ) parameter $κ= k + h^{\vee}$ where $k$ is the level number, fixed at $k = 1$, and $h^\vee$ is the dual Coxeter number for $SU(2)_L$. This leads to natural distinction between quarks and leptons in terms of a weight for the representation of $SU(2)_L$. Physical operators of the electroweak vector bosons and fermions are defined by use of Grassmann variables. Possible electroweak interactions are then determined by the evaluation of Grassmann integrals. We obtain a generating functional for the electroweak interaction vertices and illustrate how to compute decay rates of the $Z$-boson into a pair of fermions.

hep-th↗

arXiv2012

Holonomies of gauge fields in twistor space 5: amplitudes of gluons and massive scalars

Scattering amplitudes of gluons coupled with a pair of massive scalars, so-called massive scalar amplitudes, provide the simplest yet physically useful examples of massive amplitudes. In this paper we construct an S-matrix functional for the massive scalar amplitudes in a recently developed holonomy formalism in supertwistor space. From the S-matrix functional we derive ultra helicity violating (UHV), as well as next-to-UHV (NUHV), massive scalar amplitudes at tree level in a form that agrees with previously known results. We also obtain recursive expressions for non-UHV tree amplitudes in general. These results will open up a new avenue to the study of phenomenology in the spinor-helicity formalism.

hep-th↗

arXiv2012

Application of abelian holonomy formalism to the elementary theory of numbers

We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on $S^1 \times S^1 \times {\bf R}$. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of ${\bf F}_p = {\bf Z}/ p {\bf Z}$ where $p$ is an odd prime number. This enables us to calculate "scattering amplitudes" of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of "scattering" for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be useful for studies on quantum aspects of topology and number theory.

hep-th↗

arXiv2011

Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes

We consider generalization of the Cachazo-Svrcek-Witten (CSW) rules to one-loop amplitudes of N=4 super Yang-Mills theory in a recently developed holonomy formalism in twistor space. We first reconsider off-shell continuation of the Lorentz-invariant Nair measure for the incorporation of loop integrals. We then formulate an S-matrix functional for general amplitudes such that it implements the CSW rules at quantum level. For one-loop MHV amplitudes, the S-matrix functional correctly reproduces the analytic expressions obtained in the Brandhuber-Spence-Travaglini (BST) method. Motivated by this result, we propose a novel regularization scheme by use of an iterated-integral representation of polylogarithms and obtain a set of new analytic expressions for one-loop NMHV and N$^2$MHV amplitudes in a conjectural form. We also briefly sketch how the extension to one-loop non-MHV amplitudes in general can be carried out.

hep-th↗

arXiv2010

Holonomies of gauge fields in twistor space 3: gravity as a square of N=4 theory

In a recent paper, we show that an S-matrix functional for graviton amplitudes can be described by an N=8 supersymmetric gravitational holonomy operator in twistor space. In this paper, we obtain an alternative expression for the gravitational holonomy operator such that it can be interpreted as a square of an N=4 holonomy operator for frame fields, by taking a sum of certain shuffles over ordered indices. The new expression leads to amplitudes of not only spin-2 gravitons but also spin-0 massless particles. We discuss that the squared model is favored as a theory of quantum gravity.

hep-th↗

arXiv2010

Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes

We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan-Paton factor is given by a trace over elements of Poincaré algebra and Iwahori-Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan-Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.

hep-th↗

arXiv2010

Construction of Fuzzy Spaces and Their Applications to Matrix Models

Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider a mathematical aspect of fuzzy spaces, namely, their construction. We begin with a review of the construction of fuzzy complex projective spaces CP^k (k=1,2,...) in relation to geometric quantization. We then present the construction of fuzzy S^4, utilizing the fact that CP^3 is an S^2 bundle over S^4. This method is also applicable to the case of fuzzy S^8. In the second part, we consider applications of fuzzy spaces to physics. We first consider gravitational theories on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. Particularly we obtain actions for gravity on fuzzy S^2 and fuzzy CP^2. We also discuss application to M(atrix) theory. Introducing extra potentials, we show that the theory has new brane solutions whose transverse directions are described by fuzzy S^4 and fuzzy CP^3. The extra potentials can be interpreted as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. Compactification down to fuzzy S^4 is discussed and a physically interesting matrix model in four-dimensions is proposed.

hep-th↗

arXiv2010

Emergence of longitudinal 7-branes and fuzzy S^4 in compactification scenarios of M(atrix) theory

In M(atrix) theory, there exist membranes and longitudinal 5-branes (L5-branes) as extended objects. Transverse components of these brane solutions are known to be described by fuzzy CP^k (k=1,2), where k=1 and k=2 correspond to spherical membranes and L5-branes of CP^2 \times S^1 world-volume geometry, respectively. In addition to these solutions, we here show the existence of L7-branes of CP^3 \times S^1 geometry, introducing extra potentials to the M(atrix) theory Lagrangian. As in the cases of k=1,2, the L7-branes (corresponding to k=3) also break the supersymmetries of M(atrix) theory. The extra potentials are introduced such that the energy of a static L7-brane solution becomes finite in the large N limit where N represents the matrix dimension of fuzzy CP^3. As a consequence, fluctuations from the L7-branes are suppressed, which effectively describes compactification of M(atrix) theory down to 7 dimensions. We show that one of the extra potentials can be considered as a matrix-valued 7-form. The presence of the 7-form in turn supports a possibility of Freund-Rubin type compactification. This suggests that our modification of M(atrix) theory can also lead to a physically interesting matrix model in four dimensions. In hope of such a possibility, we further consider compactification of M(atrix) theory down to fuzzy S^4 which can be defined in terms of fuzzy CP^3. Along the way, we also find a new L5-brane solution to M(atrix) theory which has purely spherical geometry in the transverse directions.

hep-th↗

arXiv2009

On the deconfining limit in (2+1)-dimensional Yang-Mills theory

We consider (2+1)-dimensional Yang-Mills theory on $S^1 \times S^1 \times {\bf R}$ in the framework of a Hamiltonian approach developed by Karabali, Kim and Nair. The deconfining limit in the theory can be discussed in terms of one of the $S^1$ radii of the torus ($S^1 \times S^1$), while the other radius goes to infinity. We find that the limit agrees with the previously known result for a dynamical propagator mass of a gluon. We also make comparisons with numerical data.

hep-th↗

arXiv2009

Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes

We introduce a notion of holonomy in twistor space and construct a holonomy operator by use of a spinor-momenta formalism in twistor space. The holonomy operator gives a monodromy representation of the Knizhnik-Zamolodchikov (KZ) equation, which is mathematically equivalent to a linear representation of a braid group. We show that an S-matrix functional for gluon amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. A variety of mathematical and physical concepts, such as integrability, general covariance, Lorentz invariance and Yangian symmetry, are knit together by the holonomy operator. These results shed a new light on gauge theories in four-dimensional spacetime.

hep-th↗

arXiv2005

An interpretation of multigraviton amplitudes

We obtain alternative expressions for the multigraviton tree level amplitudes and discuss their general properties. In particular, by analogy with Yang-Mills theory, we find that some combinatoric structure can be carried by a Chan-Paton factor of general relativity as a gauge theory.

hep-th↗