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Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual

Roberto Auzzi, Prem Kumar Orcid Logo

Journal of High Energy Physics, Volume: 2008, Issue: 12, Pages: 077 - 077

Swansea University Author: Prem Kumar Orcid Logo

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DOI (Published version): 10.1088/1126-6708/2008/12/077

Abstract

<p>We study magnetic flux tubes in the Higgs vacuum of the <img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /> = 1* mass deformation of SU(<em>N</em><sub>...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2008
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URI: https://cronfa.swan.ac.uk/Record/cronfa1133
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fullrecord <?xml version="1.0"?><rfc1807><datestamp>2020-07-16T14:38:41.3902951</datestamp><bib-version>v2</bib-version><id>1133</id><entry>2012-02-23</entry><title>Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual</title><swanseaauthors><author><sid>087fd097167d724ce1b13cb285741ef5</sid><ORCID>0000-0003-0867-4213</ORCID><firstname>Prem</firstname><surname>Kumar</surname><name>Prem Kumar</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2012-02-23</date><deptcode>SPH</deptcode><abstract>&amp;#60;p&amp;#62;We study magnetic flux tubes in the Higgs vacuum of the&#xA0;&amp;#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&amp;#62;&#xA0;= 1* mass deformation of SU(&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;),&#xA0;&amp;#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&amp;#62;&#xA0;= 4 SYM and its large&#xA0;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all&#xA0;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;we identify a ``colour-flavour locked'' symmetry, SO(3)&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;C&amp;#60;/em&amp;#62;+&amp;#60;em&amp;#62;F&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;-vortex solutions carrying a&#xA0;&amp;#60;img src="http://ej.iop.org/icons/Entities/BbbZ.gif" alt="Bbb Z" align="BASELINE" /&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&amp;#60;/sub&amp;#62;-valued magnetic flux, with winding, 0&#xA0;&amp;#60;&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;&#xA0;&amp;#60;&#xA0;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;. These&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;-strings spontaneously break SO(3)&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;C&amp;#60;/em&amp;#62;+&amp;#60;em&amp;#62;F&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;to U(1)&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;C&amp;#60;/em&amp;#62;+&amp;#60;em&amp;#62;F&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;resulting in an&#xA0;&amp;#60;em&amp;#62;S&amp;#60;/em&amp;#62;&amp;#60;sup&amp;#62;2&amp;#60;/sup&amp;#62;&#xA0;moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric&#xA0;&amp;#60;img src="http://ej.iop.org/icons/Entities/BbbC.gif" alt="Bbb C" align="BASELINE" /&amp;#62;&amp;#60;img src="http://ej.iop.org/icons/Entities/BbbP.gif" alt="Bbb P" align="BASELINE" /&amp;#62;&amp;#60;sup&amp;#62;1&amp;#60;/sup&amp;#62;&#xA0;model with a theta angle &#x3B8;&amp;#60;sub&amp;#62;1+1&amp;#60;/sub&amp;#62;&#xA0;=&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;(&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#x2212;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;)&#x3B8;&amp;#60;sub&amp;#62;3+1&amp;#60;/sub&amp;#62;&#xA0;where &#x3B8;&amp;#60;sub&amp;#62;3+1&amp;#60;/sub&amp;#62;&#xA0;is the Yang-Mills vacuum angle. We find numerically that&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;-vortex tensions follow the Casimir scaling law&#xA0;&amp;#60;em&amp;#62;T&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;&amp;#60;img src="http://ej.iop.org/icons/Entities/propto.gif" alt="propto" align="BASELINE" /&amp;#62;&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;(&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#x2212;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;) for large&#xA0;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;. In the large&#xA0;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;IIB string dual, the SO(3)&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;C&amp;#60;/em&amp;#62;+&amp;#60;em&amp;#62;F&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;symmetry is manifest in the geometry interpolating between&#xA0;&amp;#60;em&amp;#62;AdS&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;5&amp;#60;/sub&amp;#62;&#xA0;&amp;#60;strong&amp;#62;&#xD7;&amp;#60;/strong&amp;#62;&#xA0;&amp;#60;em&amp;#62;S&amp;#60;/em&amp;#62;&amp;#60;sup&amp;#62;5&amp;#60;/sup&amp;#62;&#xA0;and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;-vortices as expanded probe D3-branes formed from a collection of&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;D-strings. The resulting&#xA0;&amp;#60;em&amp;#62;k&amp;#60;/em&amp;#62;-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in&#xA0;&amp;#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&amp;#62;&#xA0;= 1* theory in the large&#xA0;&amp;#60;em&amp;#62;N&amp;#60;/em&amp;#62;&amp;#60;sub&amp;#62;&amp;#60;em&amp;#62;c&amp;#60;/em&amp;#62;&amp;#60;/sub&amp;#62;&#xA0;limit.&amp;#60;/p&amp;#62;</abstract><type>Journal Article</type><journal>Journal of High Energy Physics</journal><volume>2008</volume><journalNumber>12</journalNumber><paginationStart>077</paginationStart><paginationEnd>077</paginationEnd><publisher/><issnPrint>1029-8479</issnPrint><keywords/><publishedDay>30</publishedDay><publishedMonth>11</publishedMonth><publishedYear>2008</publishedYear><publishedDate>2008-11-30</publishedDate><doi>10.1088/1126-6708/2008/12/077</doi><url/><notes/><college>COLLEGE NANME</college><department>Physics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SPH</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2020-07-16T14:38:41.3902951</lastEdited><Created>2012-02-23T17:01:56.0000000</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>Roberto</firstname><surname>Auzzi</surname><order>1</order></author><author><firstname>Prem</firstname><surname>Kumar</surname><orcid>0000-0003-0867-4213</orcid><order>2</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling 2020-07-16T14:38:41.3902951 v2 1133 2012-02-23 Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual 087fd097167d724ce1b13cb285741ef5 0000-0003-0867-4213 Prem Kumar Prem Kumar true false 2012-02-23 SPH &#60;p&#62;We study magnetic flux tubes in the Higgs vacuum of the &#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&#62; = 1* mass deformation of SU(&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;), &#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&#62; = 4 SYM and its large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62; we identify a ``colour-flavour locked'' symmetry, SO(3)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian &#60;em&#62;k&#60;/em&#62;-vortex solutions carrying a &#60;img src="http://ej.iop.org/icons/Entities/BbbZ.gif" alt="Bbb Z" align="BASELINE" /&#62;&#60;sub&#62;&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;&#60;/sub&#62;-valued magnetic flux, with winding, 0 &#60; &#60;em&#62;k&#60;/em&#62; &#60; &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;. These &#60;em&#62;k&#60;/em&#62;-strings spontaneously break SO(3)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; to U(1)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; resulting in an &#60;em&#62;S&#60;/em&#62;&#60;sup&#62;2&#60;/sup&#62; moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric &#60;img src="http://ej.iop.org/icons/Entities/BbbC.gif" alt="Bbb C" align="BASELINE" /&#62;&#60;img src="http://ej.iop.org/icons/Entities/BbbP.gif" alt="Bbb P" align="BASELINE" /&#62;&#60;sup&#62;1&#60;/sup&#62; model with a theta angle θ&#60;sub&#62;1+1&#60;/sub&#62; = &#60;em&#62;k&#60;/em&#62;(&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;−&#60;em&#62;k&#60;/em&#62;)θ&#60;sub&#62;3+1&#60;/sub&#62; where θ&#60;sub&#62;3+1&#60;/sub&#62; is the Yang-Mills vacuum angle. We find numerically that &#60;em&#62;k&#60;/em&#62;-vortex tensions follow the Casimir scaling law &#60;em&#62;T&#60;/em&#62;&#60;sub&#62;&#60;em&#62;k&#60;/em&#62;&#60;/sub&#62; &#60;img src="http://ej.iop.org/icons/Entities/propto.gif" alt="propto" align="BASELINE" /&#62; &#60;em&#62;k&#60;/em&#62;(&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;−&#60;em&#62;k&#60;/em&#62;) for large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;. In the large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62; IIB string dual, the SO(3)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; symmetry is manifest in the geometry interpolating between &#60;em&#62;AdS&#60;/em&#62;&#60;sub&#62;5&#60;/sub&#62; &#60;strong&#62;×&#60;/strong&#62; &#60;em&#62;S&#60;/em&#62;&#60;sup&#62;5&#60;/sup&#62; and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate &#60;em&#62;k&#60;/em&#62;-vortices as expanded probe D3-branes formed from a collection of &#60;em&#62;k&#60;/em&#62;D-strings. The resulting &#60;em&#62;k&#60;/em&#62;-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in &#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&#62; = 1* theory in the large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62; limit.&#60;/p&#62; Journal Article Journal of High Energy Physics 2008 12 077 077 1029-8479 30 11 2008 2008-11-30 10.1088/1126-6708/2008/12/077 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2020-07-16T14:38:41.3902951 2012-02-23T17:01:56.0000000 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Roberto Auzzi 1 Prem Kumar 0000-0003-0867-4213 2
title Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
spellingShingle Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
Prem Kumar
title_short Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
title_full Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
title_fullStr Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
title_full_unstemmed Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
title_sort Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual
author_id_str_mv 087fd097167d724ce1b13cb285741ef5
author_id_fullname_str_mv 087fd097167d724ce1b13cb285741ef5_***_Prem Kumar
author Prem Kumar
author2 Roberto Auzzi
Prem Kumar
format Journal article
container_title Journal of High Energy Physics
container_volume 2008
container_issue 12
container_start_page 077
publishDate 2008
institution Swansea University
issn 1029-8479
doi_str_mv 10.1088/1126-6708/2008/12/077
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 0
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description &#60;p&#62;We study magnetic flux tubes in the Higgs vacuum of the &#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&#62; = 1* mass deformation of SU(&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;), &#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&#62; = 4 SYM and its large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62; we identify a ``colour-flavour locked'' symmetry, SO(3)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian &#60;em&#62;k&#60;/em&#62;-vortex solutions carrying a &#60;img src="http://ej.iop.org/icons/Entities/BbbZ.gif" alt="Bbb Z" align="BASELINE" /&#62;&#60;sub&#62;&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;&#60;/sub&#62;-valued magnetic flux, with winding, 0 &#60; &#60;em&#62;k&#60;/em&#62; &#60; &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;. These &#60;em&#62;k&#60;/em&#62;-strings spontaneously break SO(3)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; to U(1)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; resulting in an &#60;em&#62;S&#60;/em&#62;&#60;sup&#62;2&#60;/sup&#62; moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric &#60;img src="http://ej.iop.org/icons/Entities/BbbC.gif" alt="Bbb C" align="BASELINE" /&#62;&#60;img src="http://ej.iop.org/icons/Entities/BbbP.gif" alt="Bbb P" align="BASELINE" /&#62;&#60;sup&#62;1&#60;/sup&#62; model with a theta angle θ&#60;sub&#62;1+1&#60;/sub&#62; = &#60;em&#62;k&#60;/em&#62;(&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;−&#60;em&#62;k&#60;/em&#62;)θ&#60;sub&#62;3+1&#60;/sub&#62; where θ&#60;sub&#62;3+1&#60;/sub&#62; is the Yang-Mills vacuum angle. We find numerically that &#60;em&#62;k&#60;/em&#62;-vortex tensions follow the Casimir scaling law &#60;em&#62;T&#60;/em&#62;&#60;sub&#62;&#60;em&#62;k&#60;/em&#62;&#60;/sub&#62; &#60;img src="http://ej.iop.org/icons/Entities/propto.gif" alt="propto" align="BASELINE" /&#62; &#60;em&#62;k&#60;/em&#62;(&#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;−&#60;em&#62;k&#60;/em&#62;) for large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62;. In the large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62; IIB string dual, the SO(3)&#60;sub&#62;&#60;em&#62;C&#60;/em&#62;+&#60;em&#62;F&#60;/em&#62;&#60;/sub&#62; symmetry is manifest in the geometry interpolating between &#60;em&#62;AdS&#60;/em&#62;&#60;sub&#62;5&#60;/sub&#62; &#60;strong&#62;×&#60;/strong&#62; &#60;em&#62;S&#60;/em&#62;&#60;sup&#62;5&#60;/sup&#62; and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate &#60;em&#62;k&#60;/em&#62;-vortices as expanded probe D3-branes formed from a collection of &#60;em&#62;k&#60;/em&#62;D-strings. The resulting &#60;em&#62;k&#60;/em&#62;-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in &#60;img src="http://ej.iop.org/icons/Entities/calN.gif" alt="Script N" align="BASELINE" /&#62; = 1* theory in the large &#60;em&#62;N&#60;/em&#62;&#60;sub&#62;&#60;em&#62;c&#60;/em&#62;&#60;/sub&#62; limit.&#60;/p&#62;
published_date 2008-11-30T03:02:50Z
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score 10.998116

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