Low Dimensional Supersymmetric Gauge Theories and Mathematical Applications

This 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics

Department dc:contributor.department

Physics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2021

Author dc:creator

• Zou, Hao

Chair dc:contributor.committeechair

• Sharpe, Eric R.

Committee members dc:contributor.committeemember

• Anderson, Lara B.
• Gray, James A.
• Barnes, Edwin Fleming

• Supersymmetric Gauge Theories
• Quantum Cohomology
• Quantum K-theory

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:30039

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/103441