Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence
Abstract By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2, 0) theory on a three-manifold M3. This generalization is applicable to both the 3d N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 1 supersymmetric reduction...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2020)101 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823863634997018624 |
|---|---|
| author | Julius Eckhard Heeyeon Kim Sakura Schäfer-Nameki Brian Willett |
| author_facet | Julius Eckhard Heeyeon Kim Sakura Schäfer-Nameki Brian Willett |
| author_sort | Julius Eckhard |
| collection | DOAJ |
| description | Abstract By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2, 0) theory on a three-manifold M3. This generalization is applicable to both the 3d N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 1 supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by M3. This is carried out in detail for M3 a Seifert manifold, where we compute a refined version of the Witten index. In the context of the 3d-3d correspondence, we complement this analysis in the dual topological theory, and determine the refined counting of flat connections on M3, which matches the Witten index computation that takes the higher-form symmetries into account. |
| format | Article |
| id | doaj-art-cadfc41e2bba47b4a141846f45a873e0 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-cadfc41e2bba47b4a141846f45a873e02025-02-09T12:05:57ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020119010.1007/JHEP01(2020)101Higher-form symmetries, Bethe vacua, and the 3d-3d correspondenceJulius Eckhard0Heeyeon Kim1Sakura Schäfer-Nameki2Brian Willett3Mathematical Institute, University of OxfordMathematical Institute, University of OxfordMathematical Institute, University of OxfordKavli Institute for Theoretical Physics, University of CaliforniaAbstract By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2, 0) theory on a three-manifold M3. This generalization is applicable to both the 3d N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 1 supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by M3. This is carried out in detail for M3 a Seifert manifold, where we compute a refined version of the Witten index. In the context of the 3d-3d correspondence, we complement this analysis in the dual topological theory, and determine the refined counting of flat connections on M3, which matches the Witten index computation that takes the higher-form symmetries into account.https://doi.org/10.1007/JHEP01(2020)101Discrete SymmetriesField Theories in Lower DimensionsM-TheorySupersymmetric Gauge Theory |
| spellingShingle | Julius Eckhard Heeyeon Kim Sakura Schäfer-Nameki Brian Willett Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence Journal of High Energy Physics Discrete Symmetries Field Theories in Lower Dimensions M-Theory Supersymmetric Gauge Theory |
| title | Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence |
| title_full | Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence |
| title_fullStr | Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence |
| title_full_unstemmed | Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence |
| title_short | Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence |
| title_sort | higher form symmetries bethe vacua and the 3d 3d correspondence |
| topic | Discrete Symmetries Field Theories in Lower Dimensions M-Theory Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP01(2020)101 |
| work_keys_str_mv | AT juliuseckhard higherformsymmetriesbethevacuaandthe3d3dcorrespondence AT heeyeonkim higherformsymmetriesbethevacuaandthe3d3dcorrespondence AT sakuraschafernameki higherformsymmetriesbethevacuaandthe3d3dcorrespondence AT brianwillett higherformsymmetriesbethevacuaandthe3d3dcorrespondence |