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dc.contributor.advisorVafa, C.
dc.contributor.authorRastogi, Ashwin
dc.date.accessioned2013-10-08T01:17:25Z
dc.date.issued2013-10-07
dc.date.submitted2013
dc.identifier.citationRastogi, Ashwin. 2013. Brane Constructions and BPS Spectra. Doctoral dissertation, Harvard University.en_US
dc.identifier.otherhttp://dissertations.umi.com/gsas.harvard:10836en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286
dc.description.abstractThe 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.en_US
dc.description.sponsorshipPhysicsen_US
dc.language.isoen_USen_US
dash.licenseLAA
dc.subjectTheoretical physicsen_US
dc.subjectParticle physicsen_US
dc.subjectBPS spectraen_US
dc.subjectgeometric engineeringen_US
dc.subjectquiveren_US
dc.subjectSeiberg-Witten theoryen_US
dc.subjectstring compactificationen_US
dc.subjecttangleen_US
dc.titleBrane Constructions and BPS Spectraen_US
dc.typeThesis or Dissertationen_US
dash.depositing.authorRastogi, Ashwin
dc.date.available2013-10-08T01:17:25Z
thesis.degree.date2013en_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.grantorHarvard Universityen_US
thesis.degree.leveldoctoralen_US
thesis.degree.namePh.D.en_US
dc.contributor.committeeMemberFranklin, Melissaen_US
dc.contributor.committeeMemberDenef, Frederiken_US
dash.contributor.affiliatedRastogi, Ashwin


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