京都大学 / 新制・課程博士 / 博士(理学) / 甲第24412号 / 理博第4911号 / 新制||理||1702(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 橋本 幸士, 准教授 福間 將文, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

While many previous studies indicated that the overall number of school string/orchestra programs in the United States has increased, string/orchestra programs have been substantially underrepresented in school music curricula. In addition, the programs have been inequitably distributed geographically, and have tended to conform particular trends in their characteristics and demographics of string teachers and students. The purpose of this study was to examine the characteristics and trends in the profile of current school string programs. Also, by investigating the inception of the programs, this study aimed to identify practical ways in creating a school string program. A 37-item questionnaire was developed to collect data. The participants were string/orchestra teachers who were teaching in public schools and members of the National Association for Music Education (NAfME). A total of 130 teachers participated in this study. The result of this study indicated that string programs remain concentrated in suburban areas. Additionally, while string student population has become more diverse and reflective of the overall student population, the racial/ethnic makeup of string teachers is still predominantly White. This study also revealed that the idea of creating a new string program was most often initiated by either school music teachers or outreach program instructors/directors, and the first step typically involves discussing the idea with school administrators.

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<p>Defended on November 3rd, 2011</p> / <p>In this thesis, we describe the properties of brane worlds embedded in a spacetime with two extra dimensions. We derive and describe the boundary conditions that branes impose on the bulk fields in the theory, and show that they reproduce known results for D7 branes in F-theory compactifications of type IIB supergravity. We show how brane-bulk couplings can stabilize moduli of a flux stabilized compactification of extra dimensions. An important new ingredient is that the branes can have a magnetic coupling to the flux that stabilizes the bulk. This coupling allows the system to relax the stringent constraints of flux quantization, which allows the bulk spacetime to respond to perturbations of the branes. We derive the dynamics of the lower-dimensional effective theory below the Kaluza-Klein scale, and show that the contributions of the magnetic coupling can be competitive with the tension of the brane. We first describe the simplest flux compactification: an Einstein-scalar- Maxwell theory in 6 dimensions. We find that the effective potential in 4 dimensions gets minimized at the position one would naively expect - at the stationary point of the sum of all the brane Lagrangians - but its value at the minimum gets changed by the magnetic coupling to the brane. Next we find that if the bulk is described by 6 dimensional gauged chiral supergravity, the effect of the magnetic coupling allows the curvature on the brane to be suppressed relative to the generic scale of the tension on the branes. We use this observation to construct an explicit brane-bulk system that has a technically natural cosmological constant of the correct size. The classical on-brane curvature vanishes in our construction, and the first order quantum corrections give a value to the cosmological constant of the right order of magnitude. We estimate higher loop corrections, and they are greatly suppressed.</p> / Doctor of Philosophy (PhD)

<p>We investigate the function ρ_<em>d</em>(<em>n</em>) = max { <em>r</em>(<em><strong>x</strong></em>) | <em><strong>x</strong></em> is a (<em>d</em>, <em>n</em>)-string } where <em>r</em>(<em><strong>x</strong></em>) is the number of runs in the string <em><strong>x</strong></em>, and a (<em>d</em>, <em>n</em>)-string is a string with length <em>n</em> and exactly <em>d</em> distinct symbols. Our investigation is motivated by the conjecture that ρ_<em>d</em>(<em>n</em>) ≤ <em>n</em>-<em>d</em>. We present and discuss fundamental properties of the ρ_<em>d</em>(<em>n</em>) function. The values of ρ_<em>d</em>(<em>n</em>) are presented in the (<em>d</em>, <em>n</em>-<em>d</em>)-table with rows indexed by <em>d</em> and columns indexed by <em>n</em>-<em>d</em> which reveals the regularities of the function. We introduce the concepts of the r-cover and core vector of a string, yielding a novel computational framework for determining ρ_<em>d</em>(<em>n</em>) values. The computation of the previously intractable instances is achieved via first computing a lower bound, and then using the structural properties to limit our exhaustive search only to strings that can possibly exceed this number of runs. Using this approach, we extended the known maximum number of runs in binary string from 60 to 74. In doing so, we find the first examples of run-maximal strings containing four consecutive identical symbols. Our framework is also applied for an arbitrary number of distinct symbols, <em>d</em>. For example, we are able to determine that the maximum number of runs in a string with 23 distinct symbols and length 46 is 23. Further, we discuss the structural properties of a shortest (<em>d</em>, <em>n</em>)-string <em><strong>x</strong></em> such that <em>r</em>(<em><strong>x</strong></em>) > <em>n</em>-<em>d</em>, should such a string exist.</p> / Doctor of Philosophy (PhD)

In this thesis we employ string perturbation theory in toroidal orbifold models to study aspects of supersymmetry breaking in type IIB string theory. First, we determine the dependence of physical Yukawa couplings on blow-up moduli in models with D3-branes at orbifold singularities. Blow-up moduli are scalar fields describing the size of small blow-up cycles in the compactification geometry. In models implementing moduli stabilisation these fields can acquire F-terms and break supersymmetry. We examine the moduli-dependence of physical Yukawa couplings at string tree-level by computing disk correlation functions involving a Yukawa interaction of visible sector fields and an arbitrary number of blow-up moduli. We perform the calculation for one blow-up insertion explicitly and find that the correlation function vanishes if the blow-up modulus is associated with a small cycle distant to the visible sector. For more than one blow-up insertion we show that all such correlation functions are exponentially suppressed by the compactification volume. We explain how these results are relevant to suppressing soft terms to scales parametrically below the gravitino mass. Further, we determine corrections to holomorphic Yukawa couplings on D3-branes at an orbifold singularity due to non-perturbative effects such as gaugino condensation on a stack of D7-branes. This can be done by calculating a one-loop threshold correction to the gauge coupling on the D7-branes. We show that, if present, the new contributions to Yukawa couplings are not aligned with the tree-level couplings. As the new Yukawa couplings contribute to soft A-terms they are sources of flavour-changing neutral currents. Last we discuss an effect unrelated to supersymmetry breaking. We show that orbifold models with D3-branes at orbifold singularities can exhibit kinetic mixing of different massless Abelian factors. For this to be possible, the relevant U(1) factors have to be associated with more than one orbifold singularity.

<p>For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level.</p><p>A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only.</p><p>We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.</p>

For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level. A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only. We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.

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