Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Bernd A. Berg, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed June 16, 2004). Includes bibliographical references.

No description available.

Thesis (Ph.D.)--Duke University, 2009.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains x, 94 p.; also includes graphics Includes bibliographical references (p. 52-54). Available online via OhioLINK's ETD Center

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The discovery of a light scalar at the Large Hadron Collider is in basic agreement with the predictions of an elementary Higgs in the Standard Model (SM). Nonetheless, a light, fundamental scalar is difficult to accommodate in the SM because quantum corrections suggest its mass should be much higher than the scale of electroweak symmetry breaking (EWSB). A natural possibility is to replace the Higgs by a strongly coupled composite. Composite dynamics also gives a natural explanation to the origin of EWSB. Phenomenologically viable composite models of EWSB are constrained by experiment to feature approximate scale invariance. This behavior may follow from near conformal dynamics. At present, lattice gauge theory (LGT) provides the only quantitative method to study near conformal composite Higgs dynamics in a fully consistent strongly coupled relativistic quantum field theory. As a novel approach to the question of finding and studying near conformal theories, I will apply LGT to the study of a generalization of Quantum ChromoDynamics (QCD) with four chiral fermion flavors plus eight flavors of finite, tunable mass. By continuously varying the mass of the eight heavy flavors, I can tune between the four flavor chirally broken theory, which exhibits features similar to QCD, and the twelve flavor theory, which is known to have a conformal fixed point. This is the "4+8 Model" for directly studying near-conformal behavior. In this dissertation, I will review modern composite phenomenology, followed by outlining a study of the 4+8 Model over a range of heavy flavor masses. As a check of near-conformal behavior, I will measure the scale dependent coupling with the method of the Wilson Flow. After verifying the existence of controllable, approximate scale invariance, I will measure the low energy particle spectrum of the 4+8 Model. This includes a Higgs-like light composite scalar. Throughout this dissertation I will make reference to LGT measurement code I wrote and contributed to the software package FUEL.

No description available.

In this thesis we are concerned with the existence of infrared fixed points and the conformal window for gauge theories with fermions. We are particularly interested in those theories that are candidates for walking technicolor. We discuss the background of technicolor and the techniques relevant to a theoretical understanding of the conformal window. Following this we extend the ideas of metric confinement and causal analyticity to theories with fermions in non-fundamental representations. We use these techniques to, respectively, provide a lower bound on the lower end of the conformal window and to provide a measure of perturbativity. As well as analytic calculations we use lattice techniques to investigate two particular candidate theories for walking technicolor - SU(2) with two adjoint fermions and with six fundamental fermions. We use Schrodinger Functional techniques to investigate the running of the theory across a wide range of scales. We measure both the running of the coupling and an estimator for the fermion mass anomalous dimension, $gamma$. We find that both theories are consistent with an infrared fixed-point. However, paying particular attention to our error estimates, we are unable to absolutely confirm their existence. This is a not unexpected result for SU(2) with two adjoint fermions but is rather surprising for SU(2) with only six fundamental fermions. In the region where we are consistent with a fixed point we find $0.05<gamma<0.56$ for $SU(2)$ with two adjoint fermions and $0.135<gamma<1.03$ for $SU(2)$ with six fundamental fermions. The measurement of $gamma$ for $SU(2)$ with two adjoint fermions is the first determination of $gamma$ for any candidate theory of walking technicolor.

Submitted by Pedro Alexandre dos Santos null (retiarus@gmail.com) on 2017-03-22T23:00:09Z No. of bitstreams: 1 dissertacao-versão-final-pedro.pdf: 1127822 bytes, checksum: 02edcd6c8cccc0fb68f13733a6af5f48 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-03-23T14:34:41Z (GMT) No. of bitstreams: 1 santos_pa_me_guara.pdf: 1127822 bytes, checksum: 02edcd6c8cccc0fb68f13733a6af5f48 (MD5) / Made available in DSpace on 2017-03-23T14:34:41Z (GMT). No. of bitstreams: 1 santos_pa_me_guara.pdf: 1127822 bytes, checksum: 02edcd6c8cccc0fb68f13733a6af5f48 (MD5) Previous issue date: 2017-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, fez-se uma introdução aos mapas dinâmicos, um conjunto de técnicas desenvolvido por Mat- sumoto, Umezawa, entre outros colaboradores, e a prescrição i na formulação usual da teoria quântica de campos no contı́nuo para descrever quebra espontânea de simetria de calibre (QES). Esta técnica baseia-se na utilização de representações unitárias não equivalentes, para construir as diferentes fases fı́sicas observadas em sistemas que apresenta QES. Introduzido o mapa dinâmico, tentou-se adaptar esta coleção de técnicas junto da prescrição i em rede, obtendo como resultado que a primeira não é satisfatoriamente desenvolvida em redes finitas, entretanto no limite termodinâmico o resultado aparenta estar adequado. Então, visitou-se o Teorema de Elitzur para as descrições obtidas por esta ferramenta, isto é, tentou-se demonstrar o Teorema de Elitzur para modelos com termos complexos provenientes da prescrição i . Uma vez que este não forneceu as informações esperadas, aplicou-se outras discussões para investigar a possibilidade da quebra espontânea de simetria de calibre em rede. Neste texto, o ferramental adotado se baseou em uma discussão apresentada por Splittorff. / In this work, an introduction to dynamic maps, a set of techniques developed by Matsumoto, Umezawa, among other collaborators, and the iepsilon prescription in the usual formulation of the quantum field theory in the continuum to describe spontaneous breaking of gauge symmetry (QES). This technique is based on the use of non-equivalent unitary representations to construct the different physical phases observed in systems that apresented QES. Introduced dynamic map, it was started the adaptation fo this collection of techniques to- gether with the prescription i in lattice, obtaining as a result that the first one is not satisfactorily developed in finite lattice, however in the thermodynamic limit the apparent result is adequate. Then the Elitzur’s The- orem was visited for the descriptions obtained by this tool, that is, it was attempted to demonstrate Elitzur’s Theorem for models with complex terms from the prescription i . As soon as the latter did not provide the expected information, other discussions were conducted to investigate the possibility of spontaneous breaking of lattice gauge symmetry. In this text, the tooling adopted was based on a discussion presented by Splittorff.

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete β functions. The motivation of calculating the discrete β functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare the distribution of Fisher zeros for lattice gauge models with four and twelve light fermion flavors. We also briefly discuss the scaling of the zeros and its connection with the infrared fixed point (IRFP) and the mass anomalous dimension. Conventional numerical simulations suffer from the critical slowing down at the critical region, which prevents one from simulating large system. In order to reach the continuum limit in the lattice gauge theories, one needs either large volume or clever extrapolations. TRG is a new computational method that may calculate exponentially large system and works well even at the critical region. We formulate the TRG blocking procedure for the two dimensional O(2) (or XY ) and O(3) spin models and discuss possible applications and generalizations of the method to other spin and lattice gauge models. We start the thesis with the introduction and historical background of the RG in general.