More on a holographic dual of QCD

We investigate the interactions among the pion, vector mesons and external gauge fields in the holographic dual of massless QCD proposed in a previous paper, hep-th/0412141, on the basis of probe D8-branes embedded in a D4-brane background in type IIA string theory. We obtain the coupling constants by performing both analytic and numerical calculations, and compare them with experimental data. It is found that the vector meson dominance in the pion form factor as well as in the Wess-Zumino-Witten term holds in an intriguing manner. We also study the \omega to \pi\gamma and \omega to 3\pi decay amplitudes. It is shown that the interactions relevant to these decay amplitudes have the same structure as that proposed by Fujiwara et al. Various relations among the masses and the coupling constants of an infinite tower of mesons are derived. These relations play crucial roles in the analysis. We find that most of the results are consistent with experiments.Comment: Latex2e, 40 pages, 6 figures, v2: references added, typos corrected, v3: PTP-style, typos corrected, v4: minor correction

Exact description of D-branes in K-matrix theory

We summarize how to describe D-branes in a matrix theory based on unstable D-instantons, which we call K-matrix theory, and explicity show that D-branes can be constructed as bound states of infinitly many unstable D-instantons. We examine the fluctuations around Dp-brane solutions in the matrix theory and show that they correctly reproduce fields on the Dp-brane world-volume. Plugging them into the action of the matrix theory, we precisely obtain the Dp-brane action as the effective action of the fluctuations.Comment: 19 pages, Talk given by S.S. at the 17th Nishinomiya-Yukawa Memorial Symposium, Nishinomiya, November, 200

Low energy hadron physics in holographic QCD

We present a holographic dual of four-dimensional, large N_c QCD with massless flavors. This model is constructed by placing N_f probe D8-branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8 - anti-D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a five-dimensional Yang-Mills theory that originates from the non-Abelian DBI action of the probe D8-brane. It is found that our model yields massless pions, which are identified with Nambu-Goldstone bosons associated with the chiral symmetry breaking. We obtain the low-energy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. Furthermore, we investigate the Chern-Simons term on the probe brane and show that it leads to the Wess-Zumino-Witten term. The mass of the \eta' meson is also considered, and we formulate a simple derivation of the \eta' mass term satisfying the Witten-Veneziano formula from supergravity.Comment: 46 pages, 1 figure, minor corrections, version to appear in Prog. Theor. Phys, v4: typos corrected, v5: The normalization of the 5d Yang-Mills action given in Eq. (5.1) is corrected. Some of the expressions in section 5 are modified accordingly, but all the conclusions remain unchange

Baryons from instantons in holographic QCD

We consider aspects of dynamical baryons in a holographic dual of QCD that is proposed on the basis of a D4/D8-brane configuration. We construct a soliton solution carrying a unit baryon number and show that it is given by an instanton solution of four-dimensional Yang-Mills theory with fixed size. The Chern-Simons term on the flavor D8-branes plays a crucial role of protecting the instanton from collapsing to zero size. By quantizing the collective coordinates of the soliton, we work out the baryon spectra. Negative-parity baryons as well as baryons with higher spins and isospins can be obtained in a simple manner.Comment: 25 pages, v2: references added, minor changes, v3: PTP-style, minor correction

Impact of lithium composition on the thermoelectric properties of the layered cobalt oxide system LixCoO2

Thermoelectric properties of the layered cobalt oxide system LixCoO2 were investigated in a wide range of Li composition, 0.98 >= x >= 0.35. Single-phase bulk samples of LixCoO2 were successfully obtained through electrochemical deintercalation of Li from the pristine LiCoO2 phase. While LixCoO2 with x >= 0.94 is semiconductive, the highly Li-deficient phase (0.75 >= x >= 0.35) exhibits metallic conductivity. The magnitude of Seebeck coefficient at 293 K (S293K) significantly depends on the Li content (x). The S293K value is as large as +70 ~ +100 uV/K for x >= 0.94, and it rapidly decreases from +90 uV/K to +10 uV/K as x is lowered within a Li composition range of 0.75 >= x >= 0.50. This behavior is in sharp contrast to the results of x <= 0.40 for which the S293K value is small and independent of x (+10 uV/K), indicating that a discontinuous change in the thermoelectric characteristics takes place at x = 0.40 ~ 0.50. The unusually large Seebeck coefficient and metallic conductivity are found to coexist in a narrow range of Li composition at about x = 0.75. The coexistence, which leads to an enhanced thermoelectric power factor, may be attributed to unusual electronic structure of the two-dimensional CoO2 block.Comment: 29 pages, 1 table, 8 figure

Preservice Teachers\u27 Understandings Related to Language in the Mathematics Classroom

Mathematics reforms are highlighting the important role that language plays in mathematics education. However, there remains a common misconception that mathematics is somehow language-free. This qualitative study explored 67 elementary preservice teachers’ developing understandings about the role of language in the mathematics classroom based on their practicum experiences. Iterative, open-coding techniques were used to analyze mentor teacher advice and preservice teachers’ observations of mentor teachers teaching a mathematics lesson. The tool helped focus preservice teachers’ attention on language in the mathematics classrooms. Implications are identified for mentor and preservice teachers’ knowledge and skill development toward linguistically responsive teaching practices

Electronic phase diagram of the layered cobalt oxide system, LixCoO2 (0.0 <= x <= 1.0)

Here we report the magnetic properties of the layered cobalt oxide system, LixCoO2, in the whole range of Li composition, 0 <= x <= 1. Based on dc-magnetic susceptibility data, combined with results of 59Co-NMR/NQR observations, the electronic phase diagram of LixCoO2 has been established. As in the related material NaxCoO2, a magnetic critical point is found to exist between x = 0.35 and 0.40, which separates a Pauli-paramagnetic and a Curie-Weiss metals. In the Pauli-paramagnetic regime (x <= 0.35), the antiferromagnetic spin correlations systematically increase with decreasing x. Nevertheless, CoO2, the x = 0 end member is a non-correlated metal in the whole temperature range studied. In the Curie-Weiss regime (x >= 0.40), on the other hand, various phase transitions are observed. For x = 0.40, a susceptibility hump is seen at 30 K, suggesting the onset of static AF order. A magnetic jump, which is likely to be triggered by charge ordering, is clearly observed at Tt = 175 K in samples with x = 0.50 (= 1/2) and 0.67 (= 2/3), while only a tiny kink appears at T = 210 K in the sample with an intermediate Li composition, x = 0.60. Thus, the phase diagram of the LixCoO2 system is complex, and the electronic properties are sensitively influenced by the Li content (x).Comment: 29 pages, 1 table, 9 figure