No Cover Image

E-Thesis 198 views 71 downloads

Exact results in supersymmetric field theory. / Thomas Kingaby

Swansea University Author: Thomas Kingaby

Abstract

This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory...

Full description

Published: 2003
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42267
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2018-08-02T18:54:17Z
last_indexed 2018-08-03T10:09:42Z
id cronfa42267
recordtype RisThesis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2018-08-02T16:24:28.6357860</datestamp><bib-version>v2</bib-version><id>42267</id><entry>2018-08-02</entry><title>Exact results in supersymmetric field theory.</title><swanseaauthors><author><sid>2caab45b0c97072e03f6ec0cd82f97fc</sid><ORCID>NULL</ORCID><firstname>Thomas</firstname><surname>Kingaby</surname><name>Thomas Kingaby</name><active>true</active><ethesisStudent>true</ethesisStudent></author></swanseaauthors><date>2018-08-02</date><abstract>This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory on a circle, we will examine the identification of this complex curve with the spectral curve of the Calogero-Moser integrable system. Since the supersymmetry restricts the perturbative contributions to the prepotential, the results we gain are exact. Further, they are independent of the compactification radius. The generalization to the quiver models, with gauge group SU(N)k, is introduced along with the spin generalization of the integrable system. The massive vacua of these theories have been determined previously, here we examine the case of a specific gauge group in order to determine the complete phase structure, including the massless vacua. We then move on to determining contributions coming from instantons to the prepotential of the theory with gauge group SU(N). We see how by lifting the theory onto 5 dimensions the functional integral on the instanton moduli space is realized as a quantum mechanical sigma-model with the moduli space as a target. However, just such a model is shown to calculate a particular index of the manifold, in this case a particular equivariant index since the space has isometries. We account for the non-compact nature of the moduli space by removing boundary terms and then calculate explicit results in the case of SU(2).</abstract><type>E-Thesis</type><journal/><journalNumber></journalNumber><paginationStart/><paginationEnd/><publisher/><placeOfPublication/><isbnPrint/><issnPrint/><issnElectronic/><keywords>Theoretical physics.</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2003</publishedYear><publishedDate>2003-12-31</publishedDate><doi/><url/><notes/><college>COLLEGE NANME</college><department>Physics</department><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><apcterm/><lastEdited>2018-08-02T16:24:28.6357860</lastEdited><Created>2018-08-02T16:24:28.6357860</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Biosciences, Geography and Physics - Physics</level></path><authors><author><firstname>Thomas</firstname><surname>Kingaby</surname><orcid>NULL</orcid><order>1</order></author></authors><documents><document><filename>0042267-02082018162441.pdf</filename><originalFilename>10797975.pdf</originalFilename><uploaded>2018-08-02T16:24:41.0530000</uploaded><type>Output</type><contentLength>3385083</contentLength><contentType>application/pdf</contentType><version>E-Thesis</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-08-02T16:24:41.0530000</embargoDate><copyrightCorrect>false</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
spelling 2018-08-02T16:24:28.6357860 v2 42267 2018-08-02 Exact results in supersymmetric field theory. 2caab45b0c97072e03f6ec0cd82f97fc NULL Thomas Kingaby Thomas Kingaby true true 2018-08-02 This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory on a circle, we will examine the identification of this complex curve with the spectral curve of the Calogero-Moser integrable system. Since the supersymmetry restricts the perturbative contributions to the prepotential, the results we gain are exact. Further, they are independent of the compactification radius. The generalization to the quiver models, with gauge group SU(N)k, is introduced along with the spin generalization of the integrable system. The massive vacua of these theories have been determined previously, here we examine the case of a specific gauge group in order to determine the complete phase structure, including the massless vacua. We then move on to determining contributions coming from instantons to the prepotential of the theory with gauge group SU(N). We see how by lifting the theory onto 5 dimensions the functional integral on the instanton moduli space is realized as a quantum mechanical sigma-model with the moduli space as a target. However, just such a model is shown to calculate a particular index of the manifold, in this case a particular equivariant index since the space has isometries. We account for the non-compact nature of the moduli space by removing boundary terms and then calculate explicit results in the case of SU(2). E-Thesis Theoretical physics. 31 12 2003 2003-12-31 COLLEGE NANME Physics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:28.6357860 2018-08-02T16:24:28.6357860 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Thomas Kingaby NULL 1 0042267-02082018162441.pdf 10797975.pdf 2018-08-02T16:24:41.0530000 Output 3385083 application/pdf E-Thesis true 2018-08-02T16:24:41.0530000 false
title Exact results in supersymmetric field theory.
spellingShingle Exact results in supersymmetric field theory.
Thomas Kingaby
title_short Exact results in supersymmetric field theory.
title_full Exact results in supersymmetric field theory.
title_fullStr Exact results in supersymmetric field theory.
title_full_unstemmed Exact results in supersymmetric field theory.
title_sort Exact results in supersymmetric field theory.
author_id_str_mv 2caab45b0c97072e03f6ec0cd82f97fc
author_id_fullname_str_mv 2caab45b0c97072e03f6ec0cd82f97fc_***_Thomas Kingaby
author Thomas Kingaby
author2 Thomas Kingaby
format E-Thesis
publishDate 2003
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory on a circle, we will examine the identification of this complex curve with the spectral curve of the Calogero-Moser integrable system. Since the supersymmetry restricts the perturbative contributions to the prepotential, the results we gain are exact. Further, they are independent of the compactification radius. The generalization to the quiver models, with gauge group SU(N)k, is introduced along with the spin generalization of the integrable system. The massive vacua of these theories have been determined previously, here we examine the case of a specific gauge group in order to determine the complete phase structure, including the massless vacua. We then move on to determining contributions coming from instantons to the prepotential of the theory with gauge group SU(N). We see how by lifting the theory onto 5 dimensions the functional integral on the instanton moduli space is realized as a quantum mechanical sigma-model with the moduli space as a target. However, just such a model is shown to calculate a particular index of the manifold, in this case a particular equivariant index since the space has isometries. We account for the non-compact nature of the moduli space by removing boundary terms and then calculate explicit results in the case of SU(2).
published_date 2003-12-31T03:52:38Z
_version_ 1763752603246657536
score 10.997956

Similar Items