Exact Results on Moduli Spaces of Supersymmetric Gauge Theories
Author(s)
Mekareeya, Noppadol
Type
Thesis
Abstract
In this thesis, certain exact results in supersymmetric gauge theories are discussed.
In these theories, holomorphic gauge invariant operators play a central role in understanding
the structure of the space of solutions to vacuum equations, known as
the moduli space. We focus on a technique to count such operators with various
quantum numbers. The counting can be done by computing a partition function,
known as the Hilbert series, which counts all holomorphic gauge invariant operators
carrying a speci ed set of global U(1) charges. The Hilbert series can be computed
exactly for various gauge theories.
In Part I of this thesis, we compute the Hilbert series of four dimensional
N = 1 supersymmetric QCD with classical gauge groups. In part II, we count chiral
operators on the one instanton moduli space on R4 and study the hypermultiplet
moduli spaces of a large class of N = 2 supersymmetric gauge theories in four
dimensions.
We demonstrate that the Hilbert series not only contains information about
the spectrum of operators in the theory, but it also carries geometrical properties of
the moduli space, e.g. the dimension. It is also an indicator of whether the moduli
space is Calabi-Yau. Moreover, Hilbert series can be used as a primary tool to test
various dualities in gauge theories and in string theory.
In these theories, holomorphic gauge invariant operators play a central role in understanding
the structure of the space of solutions to vacuum equations, known as
the moduli space. We focus on a technique to count such operators with various
quantum numbers. The counting can be done by computing a partition function,
known as the Hilbert series, which counts all holomorphic gauge invariant operators
carrying a speci ed set of global U(1) charges. The Hilbert series can be computed
exactly for various gauge theories.
In Part I of this thesis, we compute the Hilbert series of four dimensional
N = 1 supersymmetric QCD with classical gauge groups. In part II, we count chiral
operators on the one instanton moduli space on R4 and study the hypermultiplet
moduli spaces of a large class of N = 2 supersymmetric gauge theories in four
dimensions.
We demonstrate that the Hilbert series not only contains information about
the spectrum of operators in the theory, but it also carries geometrical properties of
the moduli space, e.g. the dimension. It is also an indicator of whether the moduli
space is Calabi-Yau. Moreover, Hilbert series can be used as a primary tool to test
various dualities in gauge theories and in string theory.
Date Issued
2011
Date Awarded
2011-08
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Hanany, Amihay
Sponsor
DPST and the Royal Thai Government
Creator
Mekareeya, Noppadol
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)