Unitary models in two dimensions

Unitary models in two dimensions are classes of low dimensional theories which provide us with a convenient theoretical laboratory for studying various aspects of the theory of elementary particles. In this thesis, purely bosonic U(N) sigma models with the Wess-Zuraino-Witten (WZW) term in two-dimensional Euclidean space and the supersymmetric (Susy) U(N) σ models with and without this term are discussed. Particular attention is paid to the classical solutions of the equations of motion of these models. Due to the integrabihty of these models, we can associate with them a Lax-pair formalism. We observe that solutions of the Lax-pair equations of the U(N) a model provide us with solutions of the U(N) a model with the WZW-term. This is also the case for solutions of the Susy U(N) a model with the WZW-term which can be constructed from solutions of the Lax-pair equations of the Susy U(N) σ model. We present also some explicit solutions of the Susy U(N) a model without the WZW-term. Many properties of the constructed solutions for both the purely bosonic and Susy models are explored. In particular, we calculate the values of the action for some solutions and study the stability properties of these solutions and find that all the constructed solutions of these models correspond to the saddle points of the action. Finally we consider the hnearized fermion equations in the fixed background of a bosonic field. Special attention is paid to the case when the background field is given by a solution of the U(N) σ model with and/or without the WZW-term. Some classes of solutions of this problem are presented and their properties are discussed. We observe that a class of these solutions is related to the components of the energy-momentum tensor of the purely bosonic σ model and prove that some of these solutions are traceless

Supersymmetric WZW σ\sigma Model on Full and Half Plane

We study classical integrability of the supersymmetric U(N) $\sigma$ model with the Wess-Zumino-Witten term on full and half plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit form of the first few supersymmetric charges are constructed. We show that the considered model is integrable on full plane as a concequence of the conservation of the supersymmetric charges. Also, we study the model on half plane with free boundary, and examine the conservation of the supersymmetric charges on half plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.Comment: 12 pages. submitted to IJMP

Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions

The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling limit in the noncommutative case, which turns out to be the hierarchy of a `pseudodual chiral model' in 2+1 dimensions (`pseudodual' to a hierarchy extending Ward's (modified) integrable chiral model). Applying the scaling procedure to a method generating exact solutions of a matrix (potential) KP hierarchy from solutions of a matrix linear heat hierarchy, leads to a corresponding method that generates exact solutions of the matrix dispersionless potential KP hierarchy, i.e. the pseudodual chiral model hierarchy. We use this result to construct classes of exact solutions of the su(m) pseudodual chiral model in 2+1 dimensions, including various multiple lump configurations.Comment: 37 pages, 10 figures, 2nd version: some extensions (Fig 3, Appendix A, additional references), 3rd version: some minor changes, additional reference

Quantum statistical properties of the Jaynes-Cummings model in the presence of a classical homogeneous gravitational field

The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To analyse the dynamical evolution of the atom-radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving the Schr\"{o}dinger equation in the interaction picture, the evolving state of the system is found by which the influence of the gravitational field on the dynamical behavior of the atom-radiation system is explored. Assuming that initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states, the influence of gravity on the collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.Comment: 21 page

Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I - Analytic Results for Quasinormal Modes

In this work we discuss charged rotating black holes in $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface operators in a subsector of $\mathcal{N}=4$ SYM. We add a massless uncharged scalar to the five dimensional supergravity theory, such that it still forms a consistent truncation of the type IIB ten dimensional supergravity and analyze its quasinormal modes. Separating the equation of motion to a radial and angular part, we proceed to solve the radial equation using the asymptotic matching expansion method applied to a Heun equation with two nearby singularities. We use the continued fraction method for the angular Heun equation and obtain numerical results for the quasinormal modes. In the case of the supersymmetric black hole we present some analytic results for the decay rates of the scalar perturbations. The spectrum of quasinormal modes obtained is similar to that of a chiral 1+1 CFT, which is consistent with the conjectured field-theoretic dual. In addition, some of the modes can be found analytically.Comment: 41 pages, 1 figure, LaTeX; v2: typos corrected, references adde

A longitudinal comparison of emotional, behavioral and attention problems in autistic and typically developing children

Background Mental health problems are elevated in autistic individuals but there is limited evidence on the developmental course of problems across childhood. We compare the level and growth of anxious-depressed, behavioral and attention problems in an autistic and typically developing (TD) cohort. Methods Latent growth curve models were applied to repeated parent-report Child Behavior Checklist data from age 2–10 years in an inception cohort of autistic children (Pathways, N = 397; 84% boys) and a general population TD cohort (Wirral Child Health and Development Study; WCHADS; N = 884, 49% boys). Percentile plots were generated to quantify the differences between autistic and TD children. Results Autistic children showed elevated levels of mental health problems, but this was substantially reduced by accounting for IQ and sex differences between the autistic and TD samples. There was small differences in growth patterns; anxious-depressed problems were particularly elevated at preschool and attention problems at late childhood. Higher family income predicted lower base-level on all three dimensions, but steeper increase of anxious-depressed problems. Higher IQ predicted lower level of attention problems and faster decline over childhood. Female sex predicted higher level of anxious-depressed and faster decline in behavioral problems. Social-affect autism symptom severity predicted elevated level of attention problems. Autistic girls' problems were particularly elevated relative to their same-sex non-autistic peers. Conclusions Autistic children, and especially girls, show elevated mental health problems compared to TD children and there are some differences in predictors. Assessment of mental health should be integrated into clinical practice for autistic children

A lower bound on the mass of Dark Matter particles

We discuss the bounds on the mass of Dark Matter (DM) particles, coming from the analysis of DM phase-space distribution in dwarf spheroidal galaxies (dSphs). After reviewing the existing approaches, we choose two methods to derive such a bound. The first one depends on the information about the current phase space distribution of DM particles only, while the second one uses both the initial and final distributions. We discuss the recent data on dSphs as well as astronomical uncertainties in relevant parameters. As an application, we present lower bounds on the mass of DM particles, coming from various dSphs, using both methods. The model-independent bound holds for any type of fermionic DM. Stronger, model-dependent bounds are quoted for several DM models (thermal relics, non-resonantly and resonantly produced sterile neutrinos, etc.). The latter bounds rely on the assumption that baryonic feedback cannot significantly increase the maximum of a distribution function of DM particles. For the scenario in which all the DM is made of sterile neutrinos produced via non-resonant mixing with the active neutrinos (NRP) this gives m_nrp > 1.7 keV. Combining these results in their most conservative form with the X-ray bounds of DM decay lines, we conclude that the NRP scenario remains allowed in a very narrow parameter window only. This conclusion is independent of the results of the Lyman-alpha analysis. The DM model in which sterile neutrinos are resonantly produced in the presence of lepton asymmetry remains viable. Within the minimal neutrino extension of the Standard Model (the nuMSM), both mass and the mixing angle of the DM sterile neutrino are bounded from above and below, which suggests the possibility for its experimental search.Comment: 20 pages, published in JCA

The challenges experienced by parents when parenting a child with hearing loss within a South African context

The purpose of the current study was to explore the challenges experienced by hearing parents when parenting a child with hearing loss. Using a qualitative purposive sampling design, interviews were conducted with 13 parents (9 mothers, 4 fathers) residing in Cape Town, South Africa. Four salient themes emerged, namely: 1) communication is difficult, hard, and frustrating; 2) lack of knowledge and information about hearing loss makes it difficult to parent; 3) little or no support makes for a lonely journey; and 4) support identified by parents for parents. The findings of the study have important implications for collaboration and partnerships between parents and health and family practitioners within South Africa for the design and development of supportive interventions for parents parenting a child with hearing loss

Knowledge, attitudes and practices with regard to the presence, transmission, impact, and control of cystic echinococcosis in Sidi Kacem Province, Morocco

BACKGROUND: This study is a component of a large research project on five major neglected zoonotic diseases (NZDs) including cystic echinococcosis and was undertaken in the Province of Sidi Kacem over a period of four years (April 2009-March 2013). METHODS: Questionnaires were administered at community level in a total of 27 communes and visits were made to all of the 10 abattoirs situated in the Province, to collect qualitative data on determinants of transmission for disease in humans and animals. More specifically, community knowledge, attitudes and practices related to cystic echinococcosis were assessed, as well as the extent to which local customs and behaviours may promote transmission. Abattoir infrastructure and practices, and their role in perpetuating disease transmission were also critically evaluated. RESULTS: The results show that only 50 % of people have heard of the disease, and of those, only 21 % are aware of the dog’s role in disease transmission. Sixty-seven per cent of respondents stated that dogs are fed ruminant organs deemed unfit for human consumption. Owned dogs have access to the family home, including the kitchen, in 39 % of households. The extent of this close proximity between humans and animals is even more pertinent when one considers that dogs are omnipresent in the community, with an average of 1.8 dogs owned per household. The unrestricted access of dogs to abattoirs is a huge issue, which further promotes disease transmission. CONCLUSION: This study would suggest that the high prevalence of cystic echinococcosis in humans and animals in Morocco is largely due to three factors: 1) abundance of dogs 2) engagement in risky behaviour of the local population and 3) poor abattoir infrastructure and practices. This has serious implications in terms of the socio-economic impact of the disease, especially for rural poor communities. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40249-015-0082-9) contains supplementary material, which is available to authorized users