Three-point functions in the SU(2) sector at strong coupling

Extending the methods developed in our previous works (arXiv:1110.3949, arXiv:1205.6060), we compute the three-point functions at strong coupling of the non-BPS states with large quantum numbers corresponding to the composite operators belonging to the so-called SU(2) sector in the $\mathcal{N}=4$ super-Yang-Mills theory in four dimensions. This is achieved by the semi-classical evaluation of the three-point functions in the dual string theory in the $AdS_3 \times S^3$ spacetime, using the general one-cut finite gap solutions as the external states. In spite of the complexity of the contributions from various parts in the intermediate stages, the final answer for the three-point function takes a remarkably simple form, exhibiting the structure reminiscent of the one obtained at weak coupling. In particular, in the Frolov-Tseytlin limit the result is expressed in terms of markedly similar integrals, however with different contours of integration. We discuss a natural mechanism for introducing additional singularities on the worldsheet without affecting the infinite number of conserved charges, which can modify the contours of integration.Comment: 128 pages (A summary is given in section 1); v2 minor improvement

On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors

As a step toward uncovering the relation between the weak and the strong coupling regimes of the $\mathcal{N}=4$ super Yang-Mills theory beyond the specral level, we have developed in a previous paper [arXiv:1410.8533] a novel group theoretic interpretation of the Wick contraction of the fields, which allowed us to compute a much more general class of three-point functions in the SU(2) sector, as in the case of strong coupling [arXiv:1312.3727], directly in terms of the determinant representation of the partial domain wall partition funciton. Furthermore, we derived a non-trivial identity for the three point functions with monodromy operators inserted, being the discrete counterpart of the global monodromy condition which played such a crucial role in the computation at strong coupling. In this companion paper, we shall extend our study to the entire ${\rm psu}(2,2|4)$ sector and obtain several important generalizations. They include in particular (i) the manifestly conformally covariant construction, from the basic principle, of the singlet-projection operator for performing the Wick contraction and (ii) the derivation of the monodromy relation for the case of the so-called "harmonic R-matrix", as well as for the usual fundamental R-matrtix. The former case, which is new and has features rather different from the latter, is expected to have important applications. We also describe how the form of the monodromy relation is modified as ${\rm psu}(2,2|4)$ is reduced to its subsectors.Comment: 49+10 pages;v3 Published version. Typos corrected. Explicit form of the monodromy relations for the three-point functions displaye

Novel construction and the monodromy relation for three-point functions at weak coupling

In this article, we shall develop and formulate two novel viewpoints and properties concerning the three-point functions at weak coupling in the SU(2) sector of the N = 4 super Yang-Mills theory. One is a double spin-chain formulation of the spin-chain and the associated new interpretation of the operation of Wick contraction. It will be regarded as a skew symmetric pairing which acts as a projection onto a singlet in the entire SO(4) sector, instead of an inner product in the spin-chain Hilbert space. This formalism allows us to study a class of three-point functions of operators built upon more general spin-chain vacua than the special configuration discussed so far in the literature. Furthermore, this new viewpoint has the signicant advantage over the conventional method: In the usual "tailoring" operation, the Wick contraction produces inner products between off-shell Bethe states, which cannot be in general converted into simple expressions. In contrast, our procedure directly produces the so-called partial domain wall partition functions, which can be expressed as determinants. Using this property, we derive simple determinantal representation for a broader class of three-point functions. The second new property uncovered in this work is the non-trivial identity satisfied by the three-point functions with monodromy operators inserted. Generically this relation connects three-point functions of different operators and can be regarded as a kind of Schwinger-Dyson equation. In particular, this identity reduces in the semiclassical limit to the triviality of the product of local monodromies around the vertex operators, which played a crucial role in providing all important global information on the three-point function in the strong coupling regime. This structure may provide a key to the understanding of the notion of "integrability" beyond the spectral level.Comment: 35 pages;v2 Minor corrections made. An appendix and references added;v3 Typos correcte

Direct Measurement of the Out-of-Plane Spin Texture in the Dirac Cone Surface State of a Topological Insulator

We have performed spin- and angle-resolved photoemission spectroscopy of Bi2Te3 and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface (FS) of Bi2Te3 reaches maximally 25% of the in-plane counterpart while such a sizable out-of-plane spin component does not exist in the more circular FS of TlBiSe2, indicating that the hexagonal deformation of the FS is responsible for the deviation from the ideal helical spin texture. The observed out-of-plane polarization is much smaller than that expected from existing theory, suggesting that an additional ingredient is necessary for correctly understanding the surface spin polarization in Bi2Te3.Comment: 4 pages, 3 figure

Market Maturity and Innovation

中辻卯ー教授古稀記念特

環境音と意味知識の発達との関係：5歳児がインタラクションを通して学ぶもの

It is widely believed among researchers and the general public that a close relationship exists between listening to sounds and language acquisition. However, few studies have presented evidence of this relationship, and none have focused on the effects of collaboration with and among children, which might improve their language-learning abilities. This study tried to determine the extent to which nursery school children could expand their semantic knowledge in their first language by collaborating in a small group after listening to sounds. Twenty-four nursery school children participated in this study. They were divided into eight groups and were asked to listen carefully to two sets of previously prepared sounds, each consisting of four distinct types of sounds. Both sets were developed to tell one story. After listening to all the sound sets, the children were asked to discuss and recall the order and content of each set. They were allowed to speak freely in a peer group and occasionally received positive feedback from the researcher. The results show that all the groups actively discussed and then clearly recalled the order and content of the story by working together. This finding implies that preschool children will likely also expand their semantic knowledge in a second language if input is properly delivered.音と言語獲得との関係は深いと信じられているが、実際には、そのエビデンスを示すものはほとんどない。本研究では、5歳児らが、環境音に耳をすませ、注意を向け、小グループでの話し合いの中で、言語力を伸ばしていくことを確認した。5歳児らは、ピア（仲間）とのインタラクションの中で、聴いた音を再確認し、聴いた音に対して発話する力を高めていくことができた。この研究は、母語のみならず、第二言語における習得にも応用できるかもしれない

Analytical Frameworks of the Economic Policy and Business Strategy Relations.

政府の経済政策の変化は，企業の戦略形成に大きな影響を及ぼす．その成否は，政府の政策目標と企業自らの目標に照らして，企業が，例えば，設備投資の増大，海外市場への進出，国内の雇用拡大，雇用条件の改善，新規事業への参入などといった戦略行動を決断し，実施するかどうかにかかっている．経済政策‒ 企業戦略関係は非常に込み入っており，複雑である.この論文の目的は，複雑な経済政策‒ 企業戦略関係についてその有効なあり方を議論する準備段階として，現実のそれを認識・理解するための分析フレームワークを，主としてバーナード，サイモン，ワイクの組織理論に基づきながら，探索的に考察することにある.Changes in governmental economic policy influence business firms’ strategy formation; conversely, the success or failure of economic policy depends upon whether business firms are able to realize their strategic behaviors. In other words, the relationship between economic policies and business strategies is highly complex. This article’s purpose is to search for an analytical framework of such complex relationships mainly on the basis of organizational theories by C. I. Barnard, H. A. Simon, and K. E. Weick