We determine the conditions under which half-maximal matter coupled gauged supergravity in seven dimensions admits a chiral circle reduction to yield a matter coupled gauged supergravity in six dimensions with 8 real supersymmetry. Solving these conditions we nd that the SO(2; 2) and SO(3; 1) gauged 7D supergravities give a U(1)R, and the SO(2; 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1; 4)=SO(p + 1) SO(4), with the (p + 3) axions corresponding to its abelian isometries. We then derive the necessary and sufficient conditions for the existence of a Killing spinor in N = (1; 0) gauge 6D supergravity coupled to a single tensor multiplet, vector multiplets and hypermultiplets. We show that these conditions imply most of the eld equations. We also determine the remaining equations that need to be satised by an exact solution. In this framework, we nd a novel 1=8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. The key point is that we employ an identity map between this submanifold and the internal space transverse to the string worldsheet, thereby nding a higher dimensional generalization of Gell- Mann-Zweibach tear-drop solution.

We determine the conditions under which half-maximal matter coupled gauged supergravity in seven dimensions admits a chiral circle reduction to yield a matter coupled gauged supergravity in six dimensions with 8 real supersymmetry. Solving these conditions we nd that the SO(2; 2) and SO(3; 1) gauged 7D supergravities give a U(1)R, and the SO(2; 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1; 4) / SO(p + 1) X SO(4), with the (p + 3) axions corresponding to its abelian isometries. We then derive the necessary and sufficient conditions for the existence of a Killing spinor in N = (1; 0) gauge 6D supergravity coupled to a single tensor multiplet, vector multiplets and hypermultiplets. We show that these conditions imply most of the eld equations. We also determine the remaining equations that need to be satised by an exact solution. In this framework, we nd a novel 1=8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. The key point is that we employ an identity map between this submanifold and the internal space transverse to the string worldsheet, thereby nding a higher dimensional generalization of Gell- Mann-Zweibach tear-drop solution.

Spatial patterns as well as temporal dynamics of soil moisture have a major influence on runoff generation. The investigation of these dynamics and patterns can thus yield valuable information on hydrological processes, especially in data scarce or previously ungauged catchments. The combination of spatially scarce but temporally high resolution soil moisture profiles with episodic and thus temporally scarce moisture profiles at additional locations provides information on spatial as well as temporal patterns of soil moisture at the hillslope transect scale. This approach is better suited to difficult terrain (dense forest, steep slopes) than geophysical techniques and at the same time less cost-intensive than a high resolution grid of continuously measuring sensors. Rainfall simulation experiments with dye tracers while continuously monitoring soil moisture response allows for visualization of flow processes in the unsaturated zone at these locations. Data was analyzed at different spacio-temporal scales using various graphical methods, such as space-time colour maps (for the event and plot scale) and binary indicator maps (for the long-term and hillslope scale). Annual dynamics of soil moisture and decimeterscale variability were also investigated. The proposed approach proved to be successful in the investigation of flow processes in the unsaturated zone and showed the importance of preferential flow in the Malalcahuello Catchment, a datascarce catchment in the Andes of Southern Chile. Fast response times of stream flow indicate that preferential flow observed at the plot scale might also be of importance at the hillslope or catchment scale. Flow patterns were highly variable in space but persistent in time. The most likely explanation for preferential flow in this catchment is a combination of hydrophobicity, small scale heterogeneity in rainfall due to redistribution in the canopy and strong gradients in unsaturated conductivities leading to self-reinforcing flow paths.

This thesis is devoted to a study of applications of gauged linear sigma models. First, by constructing (0,2) analogues of Hori-Vafa mirrors, we have given and checked proposals for (0,2) mirrors to projective spaces, toric del Pezzo and Hirzebruch surfaces with tangent bundle deformations, checking not only correlation functions but also e.g. that mirrors to del Pezzos are related by blowdowns in the fashion one would expect. Also, we applied the recent proposal for mirrors of non-Abelian (2,2) supersymmetric two-dimensional gauge theories to examples of two-dimensional A-twisted gauge theories with exceptional gauge groups G_2 and E_8. We explicitly computed the proposed mirror Landau-Ginzburg orbifold and derived the Coulomb ring relations (the analogue of quantum cohomology ring relations). We also studied pure gauge theories, and provided evidence (at the level of these topologicalfield-theory-type computations) that each pure gauge theory (with simply-connected gauge group) flows in the IR to a free theory of as many twisted chiral multiplets as the rank of the gauge group. Last, we have constructed hybrid Landau-Ginzburg models that RG flow to a new family of non-compact Calabi-Yau threefolds, constructed as fiber products of genus g curves and noncompact Kahler threefolds. We only considered curves given as branched double covers of P^1. Our construction utilizes nonperturbative constructions of the genus g curves, and so provides a new set of exotic UV theories that should RG flow to sigma models on Calabi-Yau manifolds, in which the Calabi-Yau is not realized simply as the critical locus of a superpotential. / Doctor of Philosophy / This thesis is devoted to a study of vacua of supersymmetric string theory (superstring theory) by gauged linear sigma models. String theory is best known as the candidate to unify Einstein’s general relativity and quantum field theory. We are interested in theories with a symmetry exchanging bosons and fermions, known as supersymmetry. The study of superstring vacua makes it possible to connect string theory to the real world, and describe the Standard model as a low energy effective theory. Gauged linear sigma models are one of the most successful models to study superstring vacua by, for example, providing insights into the global structure of their moduli spaces. We will use gauged linear sigma models to study mirror symmetry and its heterotic generalization “(0, 2) mirror symmetry.” They are both world-sheet dualities relating different interpretations of the same (internal) superstring vacua. Mirror symmetry is a very powerful duality which exchanges classical and quantum effects. By studying mirror symmetry and (0, 2) mirror symmetry, we gain more knowledge of the properties of superstring vacua.

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.

This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. Here we talk about only the most basic of their properties and give a few illustrative examples. As we wish to study collections of metric measure spaces, which are triples (X; d; m) consisting of a complete separable metric space (X; d) and a Boral probability measure m on X, there are discussions about some distances between them. Among the three that we discuss, the transportation and distortion distances were introduced by Sturm. The later, denoted by 2, on the space X2 of all metric measure spaces having finite L2-size is the focus of the second part of this thesis. The second part is an exposition based on the work done by Sturm. Here we prove a number of results on the analytic and geometric properties of (X2; 2). Beginning by noting that (X2; 2) is a non-complete space, we try to understand its completion. Towards this end, the notion of a gauged measure space is useful. These are triples (X; f; m) where X is a Polish space, m a Boral probability measure on X and f a function, also called a gauge, on X X that is symmetric and square integral with respect to the product measure m2. We show that, Theorem 1. The completion of (X2; 2) consists of all gauged measure spaces where the gauges satisfy triangle inequality almost everywhere. We denote the space of all gauged measure spaces by Y. The space X2 can be embedded in Y and the transportation distance 2 extends easily from X2 to Y. These two spaces turn out to have similar geometric properties. On both these spaces 2 is a strictly intrinsic metric; i.e. any two members in them can be joined by a shortest path. But more importantly, using a description of the geodesics in these spaces, the following result is proved. Theorem 2. Both (X2; 2) and (Y; 2) have non-negative curvature in the sense of Alexandrov.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23698号 / 理博第4788号 / 新制||理||1685(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)准教授 福間 將文, 准教授 吉岡 興一, 教授 萩野 浩一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

O estudo de inventário tem por objetivo estimar o potencial hidroelétrico de rios ou bacias, analisando várias alternativas propostas de partição de quedas, sendo que cada alternativa contém um conjunto de aproveitamentos hidroelétricos. Essas alternativas são então estudadas individualmente para definição da alternativa ótima, ou seja, a que tem melhor custo beneficio e ao mesmo tempo cause menos danos ambientais. Para essa análise necessitamos calcular a potência de cada aproveitamento específico, assim como a energia gerada, para isso então precisamos conhecer a vazão do rio em estudo, no local desses aproveitamentos. Como a vazão dos rios varia com o tempo, pois depende de variáveis como clima, geologia dos solos, desmatamento, entre outras, se recomenda usar nos cálculos séries longas de vazões médias com no mínimo 30 anos de dados, o problema é que em muitos casos não temos essas séries ou temos séries menores e incompletas, nesse caso então necessitamos estimar os valores ausentes e ruidosos utilizando os dados de estações fluviométricas próximas, para depois transportá-las para o aproveitamento em estudo, para isso utilizamos de técnicas estatísticas de correlação. A ideia nesse trabalho é de utilizarmos redes neurais artificiais ao invés das técnicas convencionais e comparar os resultados obtidos. / The inventory study aims to estimate the hydropower potential of rivers or basins, analyzing several alternative proposals for partition of falls, each of which contains a set of alternative hydroelectric developments. These alternatives are then individually analyzed to define the optimal alternative, namely that which has the best cost benefit while causing less environmental damage. For this analysis we need to calculate the power of each specific use, as well as the energy generated for that then we need to know the flow of the river under study, the location of these usages. As the river flow varies with time because it depends on variables such as climate, geology, soils, deforestation, among others, we recommend using the long series of calculations mean flow at least 30 years of data, the problem is that in many cases we do not have these series or have smaller and incomplete series, in this case then we need to estimate the missing values and noisy data using next gauged stations, and then transport them to use in the study, for this we use statistical correlation techniques. The idea is that we use work instead of the conventional Artificial Neural Network techniques and compare the results.

O estudo de inventário tem por objetivo estimar o potencial hidroelétrico de rios ou bacias, analisando várias alternativas propostas de partição de quedas, sendo que cada alternativa contém um conjunto de aproveitamentos hidroelétricos. Essas alternativas são então estudadas individualmente para definição da alternativa ótima, ou seja, a que tem melhor custo beneficio e ao mesmo tempo cause menos danos ambientais. Para essa análise necessitamos calcular a potência de cada aproveitamento específico, assim como a energia gerada, para isso então precisamos conhecer a vazão do rio em estudo, no local desses aproveitamentos. Como a vazão dos rios varia com o tempo, pois depende de variáveis como clima, geologia dos solos, desmatamento, entre outras, se recomenda usar nos cálculos séries longas de vazões médias com no mínimo 30 anos de dados, o problema é que em muitos casos não temos essas séries ou temos séries menores e incompletas, nesse caso então necessitamos estimar os valores ausentes e ruidosos utilizando os dados de estações fluviométricas próximas, para depois transportá-las para o aproveitamento em estudo, para isso utilizamos de técnicas estatísticas de correlação. A ideia nesse trabalho é de utilizarmos redes neurais artificiais ao invés das técnicas convencionais e comparar os resultados obtidos. / The inventory study aims to estimate the hydropower potential of rivers or basins, analyzing several alternative proposals for partition of falls, each of which contains a set of alternative hydroelectric developments. These alternatives are then individually analyzed to define the optimal alternative, namely that which has the best cost benefit while causing less environmental damage. For this analysis we need to calculate the power of each specific use, as well as the energy generated for that then we need to know the flow of the river under study, the location of these usages. As the river flow varies with time because it depends on variables such as climate, geology, soils, deforestation, among others, we recommend using the long series of calculations mean flow at least 30 years of data, the problem is that in many cases we do not have these series or have smaller and incomplete series, in this case then we need to estimate the missing values and noisy data using next gauged stations, and then transport them to use in the study, for this we use statistical correlation techniques. The idea is that we use work instead of the conventional Artificial Neural Network techniques and compare the results.

Zusammenfassung In den letzten Jahren haben Schwarze Löcher viel Aufmerksamkeit auf sich gezogen, insbesondere wegen ihrer ungewöhlichen quantentheoretischen Eigenschaften. Ein in diesem Zusammenhang interessantes Modell ist das geeichte SL(2,R)/U(1)-Wess-Zumino-Novikov-Witten-Modell, das im Rahmen der Stringtheorie als Euklidisches zweidimensionales Schwarzes Loch interpretiert werden kann. Die vorliegende Arbeit analysiert die klassischen Eigenschaften dieses Modells, um so die Grundlage für quantentheoretische Untersuchungen zu schaffen. Ausgangspunkt ist eine allgemeine Betrachtung über geeichte Wess-Zumino-Novikov-Witten-Modelle (WZNW-Modelle). Herkömmlicherweise werden sie mit Hilfe von Eichfeldern formuliert, deren Bewegungsgleichungen rein algebraisch sind. In der vorliegenden Arbeit werden die Eichfelder aus den Modellen eliminiert. Dabei entsteht eine Klasse von nichtlinearen integrablen konformen Feldtheorien, für deren Bewegungsgleichung eine explizite Lax-Paar-Darstellung abgeleitet wird. Diese Ergebnisse werden auf das geeichte SL(2,R)/U(1)-WZNW-Modell spezialisiert. Zum Vergleich wird auch die Eliminierung des Eichfeldes durch explizite Pfadintegration untersucht, die jedoch aufgrund mathematischer Ambiguitäten nicht zu einem abschließenden Ergebnis geführt wird. Das klassische geeichte SL(2,R)/U(1)-WZNW-Modell wird sowohl in einem unendlich ausgedehnten Minkowski-Raum als auch mit räumlich periodischen Randbedingungen untersucht. Letzteres ist für die stringtheoretische Interpretation des Modells wichtig. Es werden die nichtlinearen Bewegungsgleichungen und ihre allgemeine Lösung angegeben. Diese enthält Parameterfunktionen. Es wird ein Verfahren abgeleitet, um die Parameterfunktionen aus vorgegebenen Anfangsbedingungen zu bestimmen. Mit Hilfe dieses Verfahrens werden die Poissonklammern der Parameterfunktionen aus den kanonischen Poissonklammern der physikalischen Felder berechnet. Es wird gezeigt, daß es eine nichtlokale kanonische Transformation der nichtlinearen physikalischen Felder auf freie Felder gibt. Die entsprechende Bäcklund-Transformation wird angegeben. / Abstract In recent years, Black Holes have attracted much attention, in particular, because of their unusual quantum-theoretical properties. An interesting model, in this context, is the SL(2,R)/U(1) gauged Wess-Zumino-Novikov-Witten model, which can be interpreted stringtheoretically as Euclidean two-dimensional Black Hole. The present dissertation analyzes the classical properties of this model, in order to prepare the basis for quantum-theoretical investigations. First, gauged Wess-Zumino-Novikov-Witten (WZNW) models are intoduced in general. Usually, they are formulated including gauge fields, whose equations of motion are purely algebraic. In the present dissertation, the gauge fields are eliminated from the models. A class of non-linear integrable field theories arises, whose equations of motion can be represented by Lax pairs explicitly. These results are specialized to the SL(2,R)/U(1) gauged WZNW model. For comparison, the elimination of the gauge field by explicit path integration is also investigated. But due to mathematical ambiguities, this investigation does not lead to a final result. The classical SL(2,R)/U(1) gauged WZNW model is investigated in an infinitely extended Minkowski space-time as well as with spatially periodic boundary conditions. The latter is important for the stringtheoretical interpretation of the model. The non-linear equations of motion and their general solution are given. A procedure is derived to determine the parameter functions of the general solution from given initial conditions of the equations of motion. By means of this procedure the Poisson brackets of the parameter functions are calculated from the canonical Poisson brackets of the physical fields. It is shown that there is a non-local canonical transformation of the non-linear physical fields onto free fields. The corresponding Backlund transformation is presented.