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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
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Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Showing 1 to 5 of 5 (0.073 seconds)| 1 |
Analysis of a two-dimensional nonlinear sigma model with gravitinoWu, Ruijun 19 July 2017 (has links)
In this dissertation we considered a nonlinear sigma model with gravitino field. This is a supersymmetric extension of the nonlinear sigma model in the string theory, and we set up the geometric model using commuting variables, such that we could analyze it using the tools from calculus of variations.
We introduced an action functional which corresponds to the super harmonic map functional, which has four arguments: a map between Riemannian manifolds, a vector spinor, a Riemannian metric and a gravitino. After getting the total variation formula, we considered the symmetries that the action functional possesses. By Noether's principle these families of symmetries induces conservation laws, which help to interpret the energy-momentum tensor and the supercurrent as holomorphic sections of some complex bundle. We also discussed the supersymmetry of our model. It turns out that the supersymmetry only remains in some particular cases, which is still useful in the analysis.
Then we defined the weak solution in the distributional sense, and using Riesz potential estimates and Riviere regularity theory, we could improve the regularity of the weak solutions. More precisely, when the Riemannian metric and the gravitino are smooth, then any weak solution is actually smooth; and when the gravitino are coarse but subcritical, we can still show that the weak solutions are Holder continuous.
Next we considered the compactness of solutions with bounded energies. We showed the small energy regularity on local domains and gap properties on the global surface. We also established the Pohozaev identities and thus showed the removable singularity theorem. Finally, for a sequence of solutions of uniformly bounded energies with respect to a converging sequence of gravitino fields, we showed that they converges weakly. Actually away from finite points, the convergence is strong and at those points, the energies concentrate. After a rescaling, each of these points corresponds to finitely some Dirac-harmonic maps with curvature terms defined on the Riemann sphere. Moreover, we established the energy identities along the weakly convergent sequences modulo these bubbles.
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Chiral Rings of Two-dimensional Field Theories with (0,2) SupersymmetryGuo, Jirui 26 April 2017 (has links)
This thesis is devoted to a thorough study of chiral rings in two-dimensional (0,2) theories. We first discuss properties of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories. As a special case, we study the quantum sheaf cohomology of Grassmannians as a deformation of the usual quantum cohomology. The deformation corresponds to a (0,2) deformation of the nonabelian gauged linear sigma model whose geometric phase is associated with the Grassmannian. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. Supersymmetric localization is also applicable in this case, which proves to be efficient in computing A/2 correlation functions. We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to the Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points. As another application, we extend previous works to construct (0,2) Toda-like mirrors to the sigma model engineering Grassmannians. / Ph. D. / This thesis studies a mathematical concept called the chiral ring, which emerges from string theory. String theory is a conjectured theory that potentially unifies the existing fundamental physical laws. It has connections with many branches of mathematics, especially geometry. Spacetime is ten-dimensional in string theory, of which four dimensions are visible, and the other six are hidden at ordinary energy levels. The chiral ring encodes many geometric properties of the hidden part of spacetime. These properties can in turn affect the visible universe even at low energies. Research on chiral rings has primarily focused on a special class of geometries which have large symmetries and so are easier to handle. In order to tackle more general scenarios, we analyze the chiral rings corresponding to theories with only half the symmetry and give several new results and applications.
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On Quantum Simulators and Adiabatic Quantum AlgorithmsMostame, Sarah 22 January 2009 (has links) (PDF)
This Thesis focuses on different aspects of quantum computation theory: adiabatic quantum algorithms, decoherence during the adiabatic evolution and quantum simulators. After an overview on the area of quantum computation and setting up the formal ground for the rest of the Thesis we derive a general error estimate for adiabatic quantum computing. We demonstrate that the first-order correction, which has frequently been used as a condition for adiabatic quantum computation, does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections and shows that the computational error can be made exponentially small – which facilitates significantly shorter evolution times than the first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time of order of the inverse minimum energy gap is sufficient and necessary. Furthermore, exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grover’s search algorithm. It turns out that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits), which might limit the scalability of the system. Finally, we propose the use of electron systems to construct laboratory systems based on present-day technology which reproduce and thereby simulate the quantum dynamics of the Ising model and the O(3) nonlinear sigma model.
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On Quantum Simulators and Adiabatic Quantum AlgorithmsMostame, Sarah 28 November 2008 (has links)
This Thesis focuses on different aspects of quantum computation theory: adiabatic quantum algorithms, decoherence during the adiabatic evolution and quantum simulators. After an overview on the area of quantum computation and setting up the formal ground for the rest of the Thesis we derive a general error estimate for adiabatic quantum computing. We demonstrate that the first-order correction, which has frequently been used as a condition for adiabatic quantum computation, does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections and shows that the computational error can be made exponentially small – which facilitates significantly shorter evolution times than the first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time of order of the inverse minimum energy gap is sufficient and necessary. Furthermore, exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grover’s search algorithm. It turns out that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits), which might limit the scalability of the system. Finally, we propose the use of electron systems to construct laboratory systems based on present-day technology which reproduce and thereby simulate the quantum dynamics of the Ising model and the O(3) nonlinear sigma model.
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Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge QuotientsKatona, Gregory 01 January 2013 (has links)
Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected "Adinkraic network". Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 - > 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories.
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