Loop equations and string dualities in lattice gauge theories
Abstract/Contents
- Abstract
- The purpose of this dissertation is to explore loop equations and string dualities in lattice gauge theories. A lattice gauge theory involves a lattice, a compact Lie group, a matrix representation of the group and a parameter which is called an inverse coupling strength. The main objects of interest in the lattice gauge theories are the Wilson loop variables. A loop equation refers to expressing the expectation of a Wilson loop variable in terms of the expectations of Wilson loop sequences obtained from the loop by various loop operations. These loop equations can be used to establish the 1/N expansion of Wilson loop expectations in a strongly coupled regime. The coefficients of this expansion are represented as absolutely convergent sums over trajectories in a string theory on the lattice, establishing one kind of gauge-string duality. Finally, we will present several applications of this expansion such as the Wilson area law upper bound, the factorization property, and the correspondence of SO(N) and SU(N) Wilson loop expectations in the large N limit.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Jafarov, Jafar |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Chatterjee, Sourav |
| Thesis advisor | Chatterjee, Sourav |
| Thesis advisor | Diaconis, Persi |
| Thesis advisor | Ying, Lexing |
| Advisor | Diaconis, Persi |
| Advisor | Ying, Lexing |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jafar Jafarov. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Jafar Jafarov
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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