subject:(Seiberg Witten theory)

Harvard University

1. Rastogi, Ashwin. Brane Constructions and BPS Spectra.

Degree: PhD, Physics, 2013, Harvard University

URL: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286

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The object of this work is to exploit various constructions of string theory and M-theory to yield new insights into supersymmetric theories in both four… (more)

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The object of this work is to exploit various constructions of string theory and M-theory to yield new insights into supersymmetric theories in both four and three dimensions. In 4d, we extend work on Seiberg-Witten theory to study and compute BPS spectra of the class of complete N = 2 theories. The approach we take is based on the program of geometric engineering, in which 4d theories are constructed from compactifications of type IIB strings on Calabi-Yau manifolds. In this setup, the natural candidates for BPS states are D3 branes wrapped on supersymmetric 3-cycles in the Calabi-Yau. Our study makes use of the mathematical structure of quivers, whose representation theory encodes the notion of stability of BPS particles. Except for 11 exceptional cases, all complete theories can be constructed by wrapping stacks of two M5 branes on Riemann surfaces. By exploring the connection between quivers and M5 brane theories, we develop a powerful algorithm for computing BPS spectra, and give an in-depth study of its applications. In particular, we compute BPS spectra for all asymptotically free complete theories, as well as an infinite set of conformal (SU(2)^k) theories with certain matter content. From here, we go on to apply the insight gained from our 4d study to 3d gauge theories. We consider the analog of the M5 brane construction in the case of 3d N = 2 theories: pairs of M5 branes wrapped on a 3-manifold. Using the ansantz of R-ﬂow, we study 3-manifolds consisting of Riemann surfaces fibered over R. When the construction is non-singular, the resulting IR physics is described by a free abelian Chern-Simons theory. The mathematical data of a tangle captures the data of the gauge theory, and the Reidemeister equivalances on tangles correspond to dualities of physical descriptions. To obtain interacting matter, we allow singularities in the construction. By extending the tangle description to these singular cases, we find a set of generalized Reidemeister moves that capture non-trivial mirror symmetries of 3d gauge theories. These results give a geometric origin to these well-known 3d dualities.

Physics

Advisors/Committee Members: Vafa, C. (advisor), Franklin, Melissa (committee member), Denef, Frederik (committee member).

Subjects/Keywords: Theoretical physics; Particle physics; BPS spectra; geometric engineering; quiver; Seiberg-Witten theory; string compactification; tangle

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APA (6^th Edition):

Rastogi, A. (2013). Brane Constructions and BPS Spectra. (Doctoral Dissertation). Harvard University. Retrieved from http://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286

Chicago Manual of Style (16^th Edition):

Rastogi, Ashwin. “Brane Constructions and BPS Spectra.” 2013. Doctoral Dissertation, Harvard University. Accessed January 19, 2021. http://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286.

MLA Handbook (7^th Edition):

Rastogi, Ashwin. “Brane Constructions and BPS Spectra.” 2013. Web. 19 Jan 2021.

Vancouver:

Rastogi A. Brane Constructions and BPS Spectra. [Internet] [Doctoral dissertation]. Harvard University; 2013. [cited 2021 Jan 19]. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286.

Council of Science Editors:

Rastogi A. Brane Constructions and BPS Spectra. [Doctoral Dissertation]. Harvard University; 2013. Available from: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286

2. Veloso, Diogo. Seiberg-Witten theory on 4-manifolds with periodic ends : The philosophical discourse about God in Martin Heidegger's works.

Degree: Docteur es, Mathématiques, 2014, Aix Marseille Université

URL: http://www.theses.fr/2014AIXM4781

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Dans cette thèse on prouve des résultats analytiques sur la théorie cohomotopique de Seiberg-Witten pour des 4-variétes Riemanniennes Spinc(4) a bouts périodiques, (X,g,τ). Nos résultats… (more)

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Dans cette thèse on prouve des résultats analytiques sur la théorie cohomotopique de Seiberg-Witten pour des 4-variétes Riemanniennes Spinc(4) a bouts périodiques, (X,g,τ). Nos résultats montrent, que sur certaines conditions techniques en (X, g, τ ),, cette nouvelle version est cohérente et mène a des invariants de Seiberg-Witten.Premièrement, en utilisant le critère de Taubes pour des operateurs périodiques dans des variétes a bouts périodiques, on montre que pour une 4-varieté Riemmanienne a bouts périodiques (X, g) vérifiant certaines conditions topologiques, le Laplacian ∆+ : L2(Λ2+) → L2(Λ2+) est un opérateur de Fredholm. On prouve une décomposition de type Hodge pour des 1-formes de X, a poids positif.Ensuite on prouve, en assumant certaines conditions topologiques et courbure scalaire non-negative sur les bouts, que l'opérateur de Dirac associé a une connection périodique (ASD a l'infini) est Fredholm.Dans la deuxième partie de la thèse on démontre un isomorphisme entre le groupe de cohomologie de de Rham Hd1R(X,iR), et le groupe harmonique intervenant dans la decomposition de Hodge des 1-formes de X a poids positif. On prouve l'existence de deux séquences exactes courtes liant le groupe de jauge de l'espace de modules de Seiberg-Witten et le groupe de cohomologie H1(X, 2πiZ).Dans la troisième partie on prouve les principaux résultats: la coercitivité de l'application de Seiberg-Witten et la compacité de l'espace de moduli pour une 4-varieté a bouts périodiques (X, g, τ ), vérifiant les conditions mentionnées plus haut.Finalment, utilisant la coercivité, on montre l'existence d'un invariant cohomotopique de type Seiberg- Witten type associé a (X, g, τ ).

In this thesis we prove analytic results about a cohomotopical Seiberg-Witten theory for a Riemannian, Spinc(4) 4-manifold with periodic ends, (X,g,τ) . Our results show that, under certain technical assumptions on (X, g, τ ), this new version is coher- ent and leads to Seiberg-Witten type invariants for this new class of 4-manifolds.First, using Taubes criteria for end-periodic operators on manifolds with periodic ends, we show that, for a Riemannian 4-manifold with periodic ends (X, g), verifying certain topological conditions, the Laplacian ∆+ : L2(Λ2+) → L2(Λ2+) is a Fredholm operator. This allows us to prove an important Hodge type decomposition for positively weighted Sobolev 1-forms on X.We prove, assuming non-negative scalar curvature on each end and certain technical topological conditions, that the associated Dirac operator associated with an end-periodic connection (which is ASD at infinity) is Fredholm.In the second part of the thesis we establish an isomorphism between be- tween the de Rham cohomology group, Hd1R(X,iR) (which is a topological in- variant of X) and the harmonic group intervening in the above Hodge type decomposition of the space of positively weighted 1-forms on X. We also prove two short exact sequences relating the gauge group of our Seiberg-Witten moduli problem and the cohomology group H1(X, 2πiZ).In the third part, we…

Advisors/Committee Members: Teleman, Andrei (thesis director).

Subjects/Keywords: 4-Varieté; Théorie de Seiberg-Witten; Opérateur de Dirac; Opérateur de Fredholm; Invariant cohomotopique; 4-Manifold; Seiberg-Witten theory; Dirac operator; Fredholm operator; Cohomotopic invariant

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Veloso, D. (2014). Seiberg-Witten theory on 4-manifolds with periodic ends : The philosophical discourse about God in Martin Heidegger's works. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2014AIXM4781

Chicago Manual of Style (16^th Edition):

Veloso, Diogo. “Seiberg-Witten theory on 4-manifolds with periodic ends : The philosophical discourse about God in Martin Heidegger's works.” 2014. Doctoral Dissertation, Aix Marseille Université. Accessed January 19, 2021. http://www.theses.fr/2014AIXM4781.

MLA Handbook (7^th Edition):

Veloso, Diogo. “Seiberg-Witten theory on 4-manifolds with periodic ends : The philosophical discourse about God in Martin Heidegger's works.” 2014. Web. 19 Jan 2021.

Vancouver:

Veloso D. Seiberg-Witten theory on 4-manifolds with periodic ends : The philosophical discourse about God in Martin Heidegger's works. [Internet] [Doctoral dissertation]. Aix Marseille Université 2014. [cited 2021 Jan 19]. Available from: http://www.theses.fr/2014AIXM4781.

Council of Science Editors:

Veloso D. Seiberg-Witten theory on 4-manifolds with periodic ends : The philosophical discourse about God in Martin Heidegger's works. [Doctoral Dissertation]. Aix Marseille Université 2014. Available from: http://www.theses.fr/2014AIXM4781

Leiden University

3. Visser, Sven. Seiberg-Witten Theory.

Degree: 2013, Leiden University

URL: http://hdl.handle.net/1887/32384

► The Low energy effective Lagrangian of a supersymmetric variation of a Yang – Mills – Higgs Lagrangian, will be derived, where both Lagrangians are still N=2 supersymmetric… (more)

Subjects/Keywords: Seiberg Witten Theory; Quantum Field Theory; Supersymmetry; Yang Mills Higgs Lagrangian; Low Energy Effective Lagrangian; N=2 supersymmetric massless Lagrangian

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Visser, S. (2013). Seiberg-Witten Theory. (Masters Thesis). Leiden University. Retrieved from http://hdl.handle.net/1887/32384

Chicago Manual of Style (16^th Edition):

Visser, Sven. “Seiberg-Witten Theory.” 2013. Masters Thesis, Leiden University. Accessed January 19, 2021. http://hdl.handle.net/1887/32384.

MLA Handbook (7^th Edition):

Visser, Sven. “Seiberg-Witten Theory.” 2013. Web. 19 Jan 2021.

Vancouver:

Visser S. Seiberg-Witten Theory. [Internet] [Masters thesis]. Leiden University; 2013. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/1887/32384.

Council of Science Editors:

Visser S. Seiberg-Witten Theory. [Masters Thesis]. Leiden University; 2013. Available from: http://hdl.handle.net/1887/32384

Michigan State University

4. Knapp, Adam C. Computations of Floer homology and gauge theoretic invariants for Montesinos twins.

Degree: PhD, Department of Mathematics, 2008, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:39138

Subjects/Keywords: Mathematics; Homology theory; Gauge fields (Physics); Seiberg-Witten invariants

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Knapp, A. C. (2008). Computations of Floer homology and gauge theoretic invariants for Montesinos twins. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:39138

Chicago Manual of Style (16^th Edition):

Knapp, Adam C. “Computations of Floer homology and gauge theoretic invariants for Montesinos twins.” 2008. Doctoral Dissertation, Michigan State University. Accessed January 19, 2021. http://etd.lib.msu.edu/islandora/object/etd:39138.

MLA Handbook (7^th Edition):

Knapp, Adam C. “Computations of Floer homology and gauge theoretic invariants for Montesinos twins.” 2008. Web. 19 Jan 2021.

Vancouver:

Knapp AC. Computations of Floer homology and gauge theoretic invariants for Montesinos twins. [Internet] [Doctoral dissertation]. Michigan State University; 2008. [cited 2021 Jan 19]. Available from: http://etd.lib.msu.edu/islandora/object/etd:39138.

Council of Science Editors:

Knapp AC. Computations of Floer homology and gauge theoretic invariants for Montesinos twins. [Doctoral Dissertation]. Michigan State University; 2008. Available from: http://etd.lib.msu.edu/islandora/object/etd:39138

5. Gripp Barros Ramos, Vinicius. The asymptotics of ECH capacities and absolute gradings on Floer homologies.

Degree: Mathematics, 2013, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/3vp4q10p

► Embedded contact homology (ECH) capacities were defined by Hutchings and provide a family of obstructions to embeddings of four-dimensional symplectic manifolds. In Part I of… (more)

Subjects/Keywords: Mathematics; Contact geometry; Embedded contact homology; Heegaard Floer homology; Seiberg-Witten theory; Symplectic geometry

…disconnected. The comparison with Seiberg-Witten theory implies that this is possible only if c1… …over L of the maps (2.11). 2.4 Volume in Seiberg-Witten theory The volume enters… …x29; ∗ Here HM denotes the ‘from’ version of Seiberg-Witten Floer cohomology as defined by… …analogous map on Seiberg-Witten Floer cohomology [38]. If Y is disconnected, then there… …these to prove Proposition 2.0.3. 2.1 Seiberg-Witten Floer cohomology The proof of the…

6 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gripp Barros Ramos, V. (2013). The asymptotics of ECH capacities and absolute gradings on Floer homologies. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/3vp4q10p

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gripp Barros Ramos, Vinicius. “The asymptotics of ECH capacities and absolute gradings on Floer homologies.” 2013. Thesis, University of California – Berkeley. Accessed January 19, 2021. http://www.escholarship.org/uc/item/3vp4q10p.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gripp Barros Ramos, Vinicius. “The asymptotics of ECH capacities and absolute gradings on Floer homologies.” 2013. Web. 19 Jan 2021.

Vancouver:

Gripp Barros Ramos V. The asymptotics of ECH capacities and absolute gradings on Floer homologies. [Internet] [Thesis]. University of California – Berkeley; 2013. [cited 2021 Jan 19]. Available from: http://www.escholarship.org/uc/item/3vp4q10p.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gripp Barros Ramos V. The asymptotics of ECH capacities and absolute gradings on Floer homologies. [Thesis]. University of California – Berkeley; 2013. Available from: http://www.escholarship.org/uc/item/3vp4q10p

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

6. Klaasse, R.L. Seiberg-Witten theory for symplectic manifolds.

Degree: 2013, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/282753

► In this thesis we give an introduction to Seiberg-Witten gauge theory used to study compact oriented four-dimensional manifolds X. Seiberg-Witten theory uses a Spin c… (more)

Subjects/Keywords: Seiberg-Witten theory; four-manifolds; symplectic manifolds; Spin c structures; Dirac operators

…to Seiberg-Witten theory, while the latter is more thorough in its explanations. Lastly… …background necessary for Seiberg-Witten theory. As was mentioned in the introduction, we develop in… …Hilbert manifolds pertaining to Seiberg-Witten theory can be found in [27, Appendix A & B… …theory. Acknowledgements I would first and foremost like to thank my advisor Gil Cavalcanti… …Reinier Storm, Joost Broens and Bram Bet. Together with them I was introduced to gauge theory by…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Klaasse, R. L. (2013). Seiberg-Witten theory for symplectic manifolds. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/282753

Chicago Manual of Style (16^th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Masters Thesis, Universiteit Utrecht. Accessed January 19, 2021. http://dspace.library.uu.nl:8080/handle/1874/282753.

MLA Handbook (7^th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Web. 19 Jan 2021.

Vancouver:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Internet] [Masters thesis]. Universiteit Utrecht; 2013. [cited 2021 Jan 19]. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753.

Council of Science Editors:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Masters Thesis]. Universiteit Utrecht; 2013. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753

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