dc.contributor.advisor Vafa, C. dc.contributor.author Rastogi, Ashwin dc.date.accessioned 2013-10-08T01:17:25Z dc.date.issued 2013-10-07 dc.date.submitted 2013 dc.identifier.citation Rastogi, Ashwin. 2013. Brane Constructions and BPS Spectra. Doctoral dissertation, Harvard University. en_US dc.identifier.other http://dissertations.umi.com/gsas.harvard:10836 en dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:11148286 dc.description.abstract 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. en_US dc.description.sponsorship Physics en_US dc.language.iso en_US en_US dash.license LAA dc.subject Theoretical physics en_US dc.subject Particle physics en_US dc.subject BPS spectra en_US dc.subject geometric engineering en_US dc.subject quiver en_US dc.subject Seiberg-Witten theory en_US dc.subject string compactification en_US dc.subject tangle en_US dc.title Brane Constructions and BPS Spectra en_US dc.type Thesis or Dissertation en_US dash.depositing.author Rastogi, Ashwin dc.date.available 2013-10-08T01:17:25Z thesis.degree.date 2013 en_US thesis.degree.discipline Physics en_US thesis.degree.grantor Harvard University en_US thesis.degree.level doctoral en_US thesis.degree.name Ph.D. en_US dc.contributor.committeeMember Franklin, Melissa en_US dc.contributor.committeeMember Denef, Frederik en_US dash.contributor.affiliated Rastogi, Ashwin
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