Low Dimensional Supersymmetric Gauge Theories and Mathematical Applications

Simple item page
dc.contributor.authorZou, Haoen
dc.contributor.committeechairSharpe, Eric R.en
dc.contributor.committeememberAnderson, Lara B.en
dc.contributor.committeememberGray, James A.en
dc.contributor.committeememberBarnes, Edwin Flemingen
dc.contributor.departmentPhysicsen
dc.date.accessioned2021-05-22T08:00:39Zen
dc.date.available2021-05-22T08:00:39Zen
dc.date.issued2021-05-21en
dc.description.abstractThis thesis studies N=(2,2) gauged linear sigma models (GLSMs) and three-dimensional N=2 Chern-Simons-matter theories and their mathematical applications. After a brief review of GLSMs, we systematically study nonabelian GLSMs for symplectic and orthogonal Grassmannians, following up a proposal in the math community. As consistency checks, we have compared global symmetries, Witten indices, and Calabi-Yau conditions to geometric expectations. We also compute their nonabelian mirrors following the recently developed nonabelian mirror symmetry. In addition, for symplectic Grassmannians, we use the effective twisted superpotential on the Coulomb branch of the GLSM to calculate the ordinary and equivariant quantum cohomology of the space, matching results in the math literature. Then we discuss 3d gauge theories with Chern-Simons terms. We propose a complementary method to derive the quantum K-theory relations of projective spaces and Grassmannians from the corresponding 3d gauge theory with a suitable choice of the Chern-Simons levels. In the derivation, we compare to standard presentations in terms of Schubert cycles, and also propose a new description in terms of shifted Wilson lines, which can be generalized to symplectic Grassmannians. Using this method, we are able to obtain quantum K-theory relations, which match known math results, as well as make predictions.en
dc.description.abstractgeneralIn this thesis, we study two specific models of supersymmetric gauge theories, namely two-dimensional N=(2,2) gauged linear sigma models (GLSMs) and three-dimensional N=2 Chern-Simons-matter theories. These models have played an important role in quantum field theory and string theory for decades, and generated many fruitful results, improving our understanding of Nature by drawing on many branches in mathematics, such as complex differential geometry, intersection theory, quantum cohomology/quantum K-theory, enumerative geometry, and many others. Specifically, this thesis is devoted to studying their applications in quantum cohomology and quantum K-theory. In the first part of this thesis, we systematically study two-dimensional GLSMs for symplectic and orthogonal Grassmannians, generalizing the study for ordinary Grassmannians. By analyzing the Coulomb vacua structure of the GLSMs for symplectic Grassmannians, we are able to obtain the ordinary and equivariant quantum cohomology for these spaces. A similar methodology applies to 3d Chern-Simons-matter theories and quantum K-theory, for which we propose a new description in terms of shifted Wilson lines.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:30039en
dc.identifier.urihttp://hdl.handle.net/10919/103441en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectSupersymmetric Gauge Theoriesen
dc.subjectQuantum Cohomologyen
dc.subjectQuantum K-theoryen
dc.titleLow Dimensional Supersymmetric Gauge Theories and Mathematical Applicationsen
dc.typeDissertationen
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Zou_H_D_2021.pdf
Size:
650.42 KB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations