The appearance in string theory of higher-dimensional objects known as D-branes has been a source of much of the interesting developements in the subject during the past ten years. A very interesting phenomenon occurs when several of these D-branes are made to coincide: The abelian gauge theory living on each brane is enhanced to a non-abelian gauge theory living on the stack of coincident branes. This gives rise to interesting effects like the natural appearance of non-commutative geometry. The theory governing the dynamics of these coincident branes is still poorly understood however and only hints of the underlying structure have been seen. This thesis focuses on an attempt to better this understanding by writing down actions for coincident branes using so-called boundary fermions, originating in considerations of open strings, instead of matrices to describe the non-abelian fields. It is shown that by gauge-fixing and by suitably quantizing these boundary fermions the non-abelian action that is known, the Myers action, can be reproduced. Furthermore it is shown that under natural assumptions, unlike the Myers action, the action formulated using boundary fermions also posseses kappa-symmetry, the criterion for being the correct supersymmetric action for coincident D-branes. Another aspect of string theory discussed in this thesis is that of tensionless strings. These are of great interest for example because of their possible relation to higher spin gauge theories via the AdS/CFT-correspondence. The tensionless superstring in a plane wave background, arising as a particular limit of the near-horizon geometry of a stack of D3-branes, is considered and compared to the tensile case.

abstract: In this dissertation, I present the results from my recent investigations into the interactions involving topological defects, such as magnetic monopoles and strings, that may have been produced in the early universe. I performed numerical studies on the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. Sphaleron solution predicted by Taubes was recovered, and I mapped out its energy and size as functions of parameters. I also looked into the production, and decay modes of $U(1)$ gauge and global strings. I demonstrated that strings can be produced upon evolution of gauge wavepackets defined within a certain region of parameter space. The numerical exploration of the decay modes of cosmic string loops led to the conclusions that string loops emit particle radiation primarily due to kink collisions, and that their decay time due to these losses is proportional to $L^p$, where $L$ is the loop length and $p \approx 2$. In contrast, the decay time due to gravitational radiation scales in proportion to $L$, and I concluded that particle emission is the primary energy loss mechanism for loops smaller than a critical length scale, while gravitational losses dominate for larger loops. In addition, I analyzed the decay of cosmic global string loops due to radiation of Goldstone bosons and massive scalar ($\chi$) particles. The length of loops I studied ranges from 200-1000 times the width of the string core. I found that the lifetime of a loop is approximately $1.4L$. The energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$ is the wavenumber, and a sharp peak at $k\approx m_\chi/2$, where $m_\chi$ is the mass of $\chi$. The latter is a new feature and implies a peak at high energies (MeV-GeV) in the cosmological distribution of QCD axions. / Dissertation/Thesis / Doctoral Dissertation Physics 2020

Three problems are investigated in the context of quantum collective dynamics. First, we examine the optomechanics of a Bose-Einstein condensate trapped in an optical ring cavity and coupled to counter-propagating light fields. Virtual dipole transitions cause the light to recoil elastically from the condensate and to excite its atoms into momentum side modes. These momentum side modes produce collective density oscillations. We contrast the situation to a condensate trapped in a Fabry-Perot cavity, where only symmetric ("cosine") side modes are excited. In the ring cavity case, antisymmetric ("sine") modes can be excited also. We explore the mean field limit and find that even when the counter-propagating light fields are symmetrically pumped, there are parameter regions where spontaneous symmetry breaking occurs and the sine mode becomes occupied. In addition, quantum fluctuations are taken into account and shown to be particularly significant for parameter values near bifurcations of the mean field dynamics. The next system studied is a hybrid composed of a high quality micromechanical membrane coupled magnetically to a spinor condensate. This coupling entangles the membrane and the condensate and can produce position superposition states of the membrane. Successive spin measurements of the condensate can put the membrane into an increasingly complicated state. It is possible in principle to produce nonclassical states of the membrane. We also examine a model of weaker, nonprojective measurements of the condensate's spin using phase contrast imaging. We find an upper limit on how quickly such measurements can be made without severely disrupting the unitary dynamics. The third situation analyzed is the string breaking mechanism in ultrahigh energy collisions. When quark-antiquark pairs are produced in a collision, they are believed to be linked by a tube of chromoelectric field flux, the color string. The energy of the string grows linearly with quark separation. This energy is converted into real particles by the Schwinger mechanism. Screening of the color fields by new particles breaks the string. By quantizing excitations of the string using the conjugate coordinates of field strength and string cross-section, we recover the observed exponential spectrum of outgoing particles.

The purpose of this paper is to present the non-traditional theo- retical techniques of Erno Lendvai and introduce the application of these techniques in a detailed analysis of the Fifth String Quartet of Bela Bartok. The theories of Lendvai are based on the Fibonacci Series, a series of integers which he assigns to consecutive half-step gradations of the chromatic scale. The numbers 1,2,3,5,8... are manipulated to produce two important cornerstones of his theory, namely mi-pentatony and alpha harmonies. According to Lendvai, mi-pentatony, directly related to the Hungarian folksong idiom, is the basic scale used by Bartok. Alpha harmonies are derived by the intervallic relationships created through the use of Fibonacci numbers. Erno Lendvai's theories, although not widely known, are a partial answer to the analytical problems Bartok's music presents. His con- cepts allow for tertian chords as well as non-tertian harmonies. By basing his theories on the intervallic relationships which comprise the folksong idiom, Lendvai's theories can account for much of Bartok's music. Lendvai's theory, in contrast to traditional tonality, not only allows the tritone interval between roots of chords, but relies heavily upon it. The axis system and relative chord structures establish polar relation- ships which give the same function to chords whose roots are a tri- tone apart. Through the use of polar exchange, it is possible to shift the tonal center by six key signatures, yet never alter the function of the two polarly related chords. The analysis portion of this paper is designed to give a struc- tural, tonal and harmonic overview of each movement, giving particular attention to three areas: pentatony; relative, modally related and substitute chord harmonies; alpha harmonies. These areas assume varying degrees of importance depending on the particular movement. The theories of Lendvai are too new and untried to place them into any kind of perspective at this time. Lendvai's own writings are concerned more with a few specific pieces of Bartok's works which conform neatly to golden section principles, clear cut use of models (1:2, 1:3, 1:5), or alpha harmonies. His writings avoid thses portions of Bartok's music which defy explanation using this methodology.

Bela Bartok's six string quartets are generally regarded as the next most significant works in the medium after the quartets of Beethoven. Unlike some of his contemporaries in the field, e.g, Hindemith, Milhaud, and Schoenberg, Bartok's quartets are representative of his musical growth and, as such, are worthy of equal status with those of such recognized masters as Haydn and Mozart, as well as Beethoven...

Neste trabalho são apresentados alguns conceitos básicos da Teoria de Liouville e N=1 Super Liouville, enfatizando o cálculo das funções de três pontos dessas teorias.Uma introdução a Teoria de Campos Conformes (CFT) e a Supersimetria também sao incluídas, as quais constituem ferramentas básicas da presente pesquisa. / In this dissertation we present some basic features about Liouville and N=1 Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field Theories (CFT) and Supersymmetry, which are the basic tools of the present research.

Neste trabalho estudamos a dinâmica de partículas e cordas num campo gravitacional com métrica degenerada. Utilizamos o formalismo Hamiltoniano para determinar os vínculos da teoria e a dinâmica efetiva do sistema. Classificamos a estrutura dos vínculos de acordo com a forma de métrica e dimensão do espaço (-tempo). Obtemos também a representação das simetrias em termos de isometrias geradas por auto-vetores nulos da métrica. / In this work we stud the dynamics of particles and strings in a gravitational Field with degenerate metric. We use the Hamiltonian formalism to find out the constraints and the effective dynamics of the system. We classify the constraint structure according to the formo the me-tric and the space(time) dimension. We also obtain the representation of the symmetries in terms of the isometries generated by the null eigenvectors of the metric.

O objetivo deste trabalho é apresentar hipóteses de destacados violoncelistas e professores de violoncelo sobre o processo de aprendizagem e o ensino da técnica e da interpretação do instrumento, com a finalidade de proporcionar importantes reflexões sobre o assunto, meios de pesquisa no instrumento, alem de ser uma iniciativa de pesquisa sobre e para o meio violoncelístico brasileiro. Fundamentalmente, este trabalho consiste na apreciação da literatura especifica sobre o instrumento, produzida, na maioria das vezes, por mestres consagrados. Isso foi complementado por entrevistas e por idéias transmitidas oralmente, por meio de aulas de violoncelo (talvez o mais importante por meio de transmissão de conhecimentos musicais), alem da experiência pessoal desta autora, em sua pratica docente. Resultou desta pesquisa uma grande quantidade de dados, divergentes e convergentes, sobre os inúmeros aspectos do estudo do violoncelo, tais como: maneiras de se pensar o estudo, relaxamento, postura, respiração, escolas de técnica de arco, vibrato, mão esquerda, construção a interpretação, assim como problemas referentes ao ensino e ao estudo do violoncelo no Brasil, bem como idéias para possíveis soluções. / The goal of this to present ideas and hypothesis of remarkable cellists and professors of the cello about the learning process and the teaching of technique and interpretation of the instrument, with the objective of generating important reflections about these issues, ways of researching on the instrument, as well as being a first step towards research about and for Brazilian cellists. The ideas presented have been reached by bibliographical research, interviews, transmitted orally through cello lessons (perhaps the most important way of transmitting musical know ledge), and also obtained by the personal experience of this author over her teaching practice. A great amount of data has resulted from this research, including convergent and divergent ideas dealing with the innumerable aspects of the process of cello study, such as: ways of developing cello study, relaxation with the instrument, posture, breathing, schools of bow technique, vibrato, the left hand, construction of interpretation, problems encountered by those teaching and learning cello in Brazil, as well as ideas for possible solutions to those problems.

Neste trabalho são apresentados alguns conceitos básicos da Teoria de Liouville e N=1 Super Liouville, enfatizando o cálculo das funções de três pontos dessas teorias.Uma introdução a Teoria de Campos Conformes (CFT) e a Supersimetria também sao incluídas, as quais constituem ferramentas básicas da presente pesquisa. / In this dissertation we present some basic features about Liouville and N=1 Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field Theories (CFT) and Supersymmetry, which are the basic tools of the present research.

Neste trabalho estudamos a dinâmica de partículas e cordas num campo gravitacional com métrica degenerada. Utilizamos o formalismo Hamiltoniano para determinar os vínculos da teoria e a dinâmica efetiva do sistema. Classificamos a estrutura dos vínculos de acordo com a forma de métrica e dimensão do espaço (-tempo). Obtemos também a representação das simetrias em termos de isometrias geradas por auto-vetores nulos da métrica. / In this work we stud the dynamics of particles and strings in a gravitational Field with degenerate metric. We use the Hamiltonian formalism to find out the constraints and the effective dynamics of the system. We classify the constraint structure according to the formo the me-tric and the space(time) dimension. We also obtain the representation of the symmetries in terms of the isometries generated by the null eigenvectors of the metric.