Type
Text
Type
Dissertation
Advisor
van Nieuwenhuizen, Peter | Rocek, Martin | Herzog, Christopher | Hemmick, Thomas | Lawson, Blaine.
Date
2013-12-01
Keywords
Complex Geometry, Quantum Field Theory, Supersymmetry | Physics
Department
Department of Physics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76690
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In this dissertation we study various aspects of Supersymmetric Quantum Field Theory and Complex Geometry. We focus on three main aspects. The first is general N=(2,2) gauged linear sigma models involving semichiral fields. We show that integrating out the semichiral vector multiplet leads to the generalized potential for a hyperkahler manifold, providing a formulation of the hyperkahler quotient in a generalized setting. We then discuss a new quotient construction which leads to non-Kahler manifolds. The second problem we study is motivated by recent developments in the study of the Coulomb branch of supersymmetric theories with a hyperkahler moduli space. A crucial element in these developments is the expression for Darboux coordinates in the hyperkahler manifold. We give a simple derivation of this expression by using projective superspace techniques and we apply this to the study of the moduli space of theories with eight supercharges on R^3 x S^1 and R^3 x T^2. Finally, we study the partition function of three-dimensional Chern-Simons theories on S^3 with affine ADE quivers. We give a general formula for the partition function of affine D-type quivers in terms of the Chern-Simons levels, providing a prediction for the volume of an infinite family of tri-Sasaki Einstein manifolds corresponding to the gravitational duals of such field theories. | 148 pages
Recommended Citation
Crichigno, Patricio Marcos, "Aspects of Supersymmetric Field Theories and Complex Geometry" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2574.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2574