G-Extensions of Quantum Group Categories and Functorial SPT
In this short mostly expository note, we sketch a program for gauging fully extended topological field theories in 3 dimensions. One begins with the spherical fusion category with which one wants to do Levin-Wen or Turaev-Viro. One then computes a homotopic space with certain $\pi_\bullet$ given by...
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| creator | Husain, Ammar |
| description | In this short mostly expository note, we sketch a program for gauging fully
extended topological field theories in 3 dimensions. One begins with the
spherical fusion category with which one wants to do Levin-Wen or Turaev-Viro.
One then computes a homotopic space with certain $\pi_\bullet$ given by
autoequivalences, invertible objects and the ground (algebraic) field. Then for
each desired symmetry group $G$ one looks at mapping $BG$ into that. This
classifies equivalence classes of G-extended fusion categories. This is an
equivalence at a fully extended level so will allow many defects rather than
only evaluating partition functions on closed manifolds. We can now use these
categories to build a new fully extended 3d topological field theory, but now
possibly with extra data. This is the result of permeating defect walls and
saying how that affects the assignment to the point strata. |
| doi_str_mv | 10.48550/arxiv.1605.08398 |
| format | Article |
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extended topological field theories in 3 dimensions. One begins with the
spherical fusion category with which one wants to do Levin-Wen or Turaev-Viro.
One then computes a homotopic space with certain $\pi_\bullet$ given by
autoequivalences, invertible objects and the ground (algebraic) field. Then for
each desired symmetry group $G$ one looks at mapping $BG$ into that. This
classifies equivalence classes of G-extended fusion categories. This is an
equivalence at a fully extended level so will allow many defects rather than
only evaluating partition functions on closed manifolds. We can now use these
categories to build a new fully extended 3d topological field theory, but now
possibly with extra data. This is the result of permeating defect walls and
saying how that affects the assignment to the point strata.</description><identifier>DOI: 10.48550/arxiv.1605.08398</identifier><language>eng</language><subject>Mathematics - Quantum Algebra ; Physics - Strongly Correlated Electrons</subject><creationdate>2016-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1605.08398$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1605.08398$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Husain, Ammar</creatorcontrib><title>G-Extensions of Quantum Group Categories and Functorial SPT</title><description>In this short mostly expository note, we sketch a program for gauging fully
extended topological field theories in 3 dimensions. One begins with the
spherical fusion category with which one wants to do Levin-Wen or Turaev-Viro.
One then computes a homotopic space with certain $\pi_\bullet$ given by
autoequivalences, invertible objects and the ground (algebraic) field. Then for
each desired symmetry group $G$ one looks at mapping $BG$ into that. This
classifies equivalence classes of G-extended fusion categories. This is an
equivalence at a fully extended level so will allow many defects rather than
only evaluating partition functions on closed manifolds. We can now use these
categories to build a new fully extended 3d topological field theory, but now
possibly with extra data. This is the result of permeating defect walls and
saying how that affects the assignment to the point strata.</description><subject>Mathematics - Quantum Algebra</subject><subject>Physics - Strongly Correlated Electrons</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqwkAYRmfjomgfoCvnBRLnkmR-cSVB04Kgovvwz00COpFJUvTtbdXV4dscvkPIF2dpBnnOZhhvzW_KC5anDOQcPsiiSla33oWuaUNHW0_3A4Z-uNAqtsOVlti7Uxsb11EMlq6HYPq_iWd62B0nZOTx3LnPN8fksF4dy-9ks61-yuUmwUJBYjMPBWfGKm-szvJCKiucNoajFF5bBK60BECnLRcOrFAgtBLoJTBQckymL-vzfH2NzQXjvf6PqJ8R8gE5TkH5</recordid><startdate>20160526</startdate><enddate>20160526</enddate><creator>Husain, Ammar</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160526</creationdate><title>G-Extensions of Quantum Group Categories and Functorial SPT</title><author>Husain, Ammar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-d4f8610cd7fcdb45637d2ebcc1a32fbda817b388aebd12e8d2782b72af380873</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics - Quantum Algebra</topic><topic>Physics - Strongly Correlated Electrons</topic><toplevel>online_resources</toplevel><creatorcontrib>Husain, Ammar</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Husain, Ammar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>G-Extensions of Quantum Group Categories and Functorial SPT</atitle><date>2016-05-26</date><risdate>2016</risdate><abstract>In this short mostly expository note, we sketch a program for gauging fully
extended topological field theories in 3 dimensions. One begins with the
spherical fusion category with which one wants to do Levin-Wen or Turaev-Viro.
One then computes a homotopic space with certain $\pi_\bullet$ given by
autoequivalences, invertible objects and the ground (algebraic) field. Then for
each desired symmetry group $G$ one looks at mapping $BG$ into that. This
classifies equivalence classes of G-extended fusion categories. This is an
equivalence at a fully extended level so will allow many defects rather than
only evaluating partition functions on closed manifolds. We can now use these
categories to build a new fully extended 3d topological field theory, but now
possibly with extra data. This is the result of permeating defect walls and
saying how that affects the assignment to the point strata.</abstract><doi>10.48550/arxiv.1605.08398</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Quantum Algebra Physics - Strongly Correlated Electrons |
| title | G-Extensions of Quantum Group Categories and Functorial SPT |
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