88,193 research outputs found
Topological Quantum Field Theory and the Geometric Langlands Correspondence
No full textIn the pioneering work of A. Kapustin and E. Witten, the geometric Langlands program of number theory was shown to be intimately related to duality of GL-twisted N=4 super Yang-Mills theory compactified on a Riemann surface. In this thesis, we generalize Kapustin-Witten by investigating compactification of the GL-twisted theory to three dimensions on a circle (for various values of the twisting parameter t). By considering boundary conditions in the three-dimensional description, we classify codimension-two surface operators of the GL-twisted theory, generalizing those surface operators studied by S. Gukov and E. Witten. For t=i, we propose a complete description of the 2-category of surface operators in terms of module categories, and, in addition, we determine the monoidal category of line operators which includes Wilson lines as special objects. For t=1 and t=0, we discuss surface and line operators in the abelian case.
We generalize Kapustin-Witten also by analyzing a separate twisted version of N=4, the Vafa-Witten theory. After introducing a new four-dimensional topological gauge theory, the gauged 4d A-model, we locate the Vafa-Witten theory as a special case. Compactification of the Vafa-Witten theory on a circle and on a Riemann surface is discussed. Several novel two- and three-dimensional topological gauge theories are studied throughout the thesis and in the appendices.
In work unrelated to the main thread of the thesis, we conclude by classifying codimension-one topological defects in two-dimensional sigma models with various amounts of supersymmetry.</p
The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of
No full textIn 2004, W.D. Neumann showed that the complex hyperbolic volume of a hyperbolic 3-manifold M can be obtained as the image of the Dijkgraaf-Witten invariant of M by a certain 3-cocycle. After that, C.K. Zickert gave an analogue of the Neumann's work for free fields containing finite fields. The author formulated a simple method to calculate a weaker version of the Zickert's analogue, called the reduced Dijkgraaf-Witten invariant, for finite fields and gave a formula for twist knot complements and in his previous work. In this paper, we show concretely how to calculate the reduced Dijkgraaf-Witten invariants of double twist knot complements and , and give a formula of them for p = 7
Horst F. Rupp, Susanne Schwarz (Hg.), Lebensweg, religiöse Erziehung und Bildung. Religionspädagogik als Autobiographie, Band 7. Würzburg: Königshausen & Neumann, 2020. (= Forum zur Pädagogik und Didaktik der Religion, Neue Folge Band 9)
No full textWitten U. Horst F. Rupp, Susanne Schwarz (Hg.), Lebensweg, religiöse Erziehung und Bildung. Religionspädagogik als Autobiographie, Band 7. Würzburg: Königshausen & Neumann, 2020. (= Forum zur Pädagogik und Didaktik der Religion, Neue Folge Band 9). Theologische Literaturzeitung . 01.07.2022;147(7)
Connection matrices via the Morse-Witten
No full textOrientador: Ketty Abaroa de RezendeDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação CientíficaResumo: Dada uma variedade suave e fechada M, o complexo de Morse-Witten associado a uma função de Morse f : M ? R e a uma métrica Riemanniana g em M consiste de grupos de cadeia gerados pelos pontos críticos de f e um operador bordo que conta linhas de fluxos isoladas do fluxo gradiente negativo. A homologia do complexo de Morse-Witten é isomorfa à homologia singular de M. Dado um conjunto invariante isolado S, uma matriz de conexão para uma decomposição de Morse de S é uma matriz de homomorfismos entre os índices homológicos de Conley dos conjuntos de Morse. A matriz de conexão é capaz de prover informações dinâmicas sobre um fluxo. De fato, esta matriz pode detectar a existência de órbitas conectantes entre os conjuntos de Morse de S. O complexo de Morse-Witten está relacionado à teoria de matrizes de conexão. Mais precisamente, o operador bordo do complexo de Morse-Witten é um caso especial de matriz de conexãoAbstract: Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f : M ? R and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. The homology of the Morse-Witten complex is isomorphic to the singular homology of M. Give a isolated invariant set S, a connection matrix for a Morse decomposition of S is a matrix of homomorphism between the Conley homology indices of Morse sets. The connection matrix is capable of providing dynamical information of a flow. In fact, this matrix can detect the existence of connecting orbits among Morse sets of S: The Morse-Witten complex is related to connection matrices theory. More precisely, the boundary operator of the Morse-Witten complex is a special case of connection matrixMestradoMatematicaMestre em Matemátic
First results about effects of an amino acid optimized diet on growth parameters of young warm blooded stallions
No full textFirst results about effects of an amino acid optimized diet on growth parameters of young warm blooded stallions
No full textSemiklassische Spektraltheorie von diskreten Witten-Laplace-Operatoren
No full textA discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.In dieser Arbeit wird auf dem n-dimensionalen Gitter der ganzen Zahlen ein Analogon des Witten-Laplace-Operatoren eingeführt. Nach geeigneter Skalierung des Gitters und des Operatoren analysieren wir den Tunneleffekt zwischen verschiedenen Potentialtöpfen und erhalten vollständige Aymptotiken für das tiefliegende Spektrum. Der Beweis (nach Methoden, die von B. Helffer, M. Klein und F. Nier im Falle des kontinuierlichen Witten-Laplace-Operatoren entwickelt wurden) basiert auf der Konstruktion eines diskreten Witten-Komplexes und der Analyse des zugehörigen Witten-Laplace-Operatoren auf 1-Formen. Das Resultat kann im Kontext von metastabilen Markov Prozessen auf dem Gitter reformuliert werden und ermöglicht scharfe Aussagen über metastabile Austrittszeiten
Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces
No full textLet F be a differentiable manifold endowed with an almost Kähler structure (J,ω), α a J-holomorphic action of a compact Lie group on F, and K a closed normal subgroup of which leaves ω invariant.
The purpose of this article is to introduce gauge theoretical invariants for such triples (F,α,K). The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface Σ.
Our main results concern the special case of the triple
where αcan denotes the canonical action of on . We give a complex geometric interpretation of the corresponding moduli spaces of solutions in terms of gauge theoretical quot spaces, and compute the invariants explicitly in the case r=1.
Proving a comparison theorem for virtual fundamental classes, we show that the full Seiberg–Witten invariants of ruled surfaces, as defined in [OT2], can be identified with certain gauge theoretical Gromov–Witten invariants of the triple (Hom(ℂ,ℂ< r 0),αcan, U(1)). We find the following formula for the full Seiberg–Witten invariant of a ruled surface over a Riemann surface of genus g:
where [F] denotes the class of a fibre. The computation of the invariants in the general case r >1 should lead to a generalized Vafa-Intriligator formula for “twisted”Gromov–Witten invariants associated with sections in Grassmann bundles
Topological invariance of the Witten index
No full textAbstractWe discuss the Witten index in terms of Krein's spectral shift function, and prove invariance of the Witten index under suitable relative trace class hypotheses
Semiclassical spectral analysis of discrete Witten Laplacians
No full textA discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice
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