TitleTopological string, supersymmetric gauge theory and BPS counting
NamePan, Guang (author), Diaconescu, Duiliu-Emanuel (chair), Moore, Gregory (internal member), Lukyanov, Sergei (internal member), Yuzbashyan, Emil (internal member), Neitzke, Andrew (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectPhysics and Astronomy,
DescriptionIn this thesis we study the Donaldson-Thomas theory on the local curve geometry, which arises in the context of geometric engineering of supersymmetric gauge theory from type IIA string compactification. The topological A-model amplitude gives the F-term interaction of the com- pactified theory. In particular, it is related to the instanton partition function via Nekrasov conjecture. We will introduce ADHM sheaves on curve, as an alternative description of local Donaldson-Thomas theory. We derive the wallcrossing of ADHM invariants and their refinements. We show that it is equivalent to the semi-primitive wallcrossing from supergravity, and the Kontsevich-Soibelman wallcrossing formula. As an application, we discuss the connection between ADHM moduli space with Hitchin system. In particular we give a recursive formula for the Poincare polynomial of Hitchin system in terms of instanton partition function, from refined wallcrossing. We also introduce higher rank generalization of Donaldson-Thomas invariant in the context of ADHM sheaves. We study their wallcrossing and discuss their physical interpretation via string duality.
NoteIncludes bibliographical references
Noteby Guang Pan
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.