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dc.contributor.advisorNeitzke, Andrewen
dc.contributor.advisorDistler, Jacquesen
dc.creatorMainiero, Thomas Josephen
dc.date.accessioned2015-10-09T18:37:07Zen
dc.date.available2015-10-09T18:37:07Zen
dc.date.issued2015-05en
dc.date.submittedMay 2015en
dc.identifierdoi:10.15781/T27881en
dc.identifier.urihttp://hdl.handle.net/2152/31637en
dc.descriptiontexten
dc.description.abstractThe BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry (a theory of class S(A)) exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of BPS-indices with the charge is exponential. We show this using spectral networks and, independently, using wall-crossing formulae and quiver methods. The technique using spectral networks hints at a general property dubbed "algebraicity": generating series for BPS-indices in theories of class S(A) (a class of N=2 four-dimensional field theories) are secretly algebraic functions over the rational numbers. Kontsevich and Soibelman have an independent understanding of algebraicity using indirect techniques, however, spectral networks give a distinct reason for algebraicity with the advantage of providing explicit algebraic equations obeyed by generating series; along these lines, we provide a novel example of such an algebraic equation, and explore some relationships to Euler characteristics of Kronecker quiver stable moduli. We conclude by proving that exponential asymptotic growth is a corollary of algebraicity, leading to the slogan "there are either finitely many BPS indices or exponentially many" (in theories of class S(A)).en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.subjectN=2 supersymmetryen
dc.subjectBPS-indicesen
dc.subjectDonaldson-Thomas invariantsen
dc.subjectTheories of class sen
dc.subjectSU(3) super yang millsen
dc.subjectKontsevich and Soibelman wall crossing formulaen
dc.subjectWild wall crossingen
dc.subjectSpectral networksen
dc.subjectAlgebraic generating seriesen
dc.subjectExponential degeneracyen
dc.subjectAsymptotics of BPS-indicesen
dc.titleBeyond wild walls there is algebraicity and exponential growth (of BPS indices)en
dc.typeThesisen
dc.date.updated2015-10-09T18:37:07Zen
dc.contributor.committeeMemberKaplunovsky, Vadimen
dc.contributor.committeeMemberFischler, Willyen
dc.contributor.committeeMemberKeel, Seanen
dc.description.departmentPhysicsen
thesis.degree.departmentPhysicsen
thesis.degree.disciplinePhysicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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