Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities
Abstract We study the topologically twisted index of 3d N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Gröbner basis algorithm for computing the Σ g × S 1 index explicitly and exactly in terms of the associated Bethe ideal, which is defined as the alg...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2023)148 |
| _version_ | 1797736474142048256 |
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| author | Cyril Closset Osama Khlaif |
| author_facet | Cyril Closset Osama Khlaif |
| author_sort | Cyril Closset |
| collection | DOAJ |
| description | Abstract We study the topologically twisted index of 3d N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Gröbner basis algorithm for computing the Σ g × S 1 index explicitly and exactly in terms of the associated Bethe ideal, which is defined as the algebraic ideal associated with the Bethe equations of the corresponding 3d A-model. We then revisit recently discovered infrared dualities for unitary SQCD with gauge group U(N c ) k,k+lNc with l ≠ 0, namely the Nii duality that generalises the Giveon-Kutasov duality, the Amariti-Rota duality that generalises the Aharony duality, and their further generalisations in the case of arbitrary numbers of fundamental and antifundamental chiral multiplets. In particular, we determine all the flavour Chern-Simons contact terms needed to make these dualities work. This allows us to check that the twisted indices of dual theories match exactly. We also initiate the study of the Witten index of unitary SQCD with l ≠ 0. |
| first_indexed | 2024-03-12T13:14:23Z |
| format | Article |
| id | doaj.art-415e13a760fc4ad7b6eeaa1a082bfcc0 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:14:23Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-415e13a760fc4ad7b6eeaa1a082bfcc02023-08-27T11:04:33ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023515010.1007/JHEP05(2023)148Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualitiesCyril Closset0Osama Khlaif1School of Mathematics, University of BirminghamSchool of Mathematics, University of BirminghamAbstract We study the topologically twisted index of 3d N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Gröbner basis algorithm for computing the Σ g × S 1 index explicitly and exactly in terms of the associated Bethe ideal, which is defined as the algebraic ideal associated with the Bethe equations of the corresponding 3d A-model. We then revisit recently discovered infrared dualities for unitary SQCD with gauge group U(N c ) k,k+lNc with l ≠ 0, namely the Nii duality that generalises the Giveon-Kutasov duality, the Amariti-Rota duality that generalises the Aharony duality, and their further generalisations in the case of arbitrary numbers of fundamental and antifundamental chiral multiplets. In particular, we determine all the flavour Chern-Simons contact terms needed to make these dualities work. This allows us to check that the twisted indices of dual theories match exactly. We also initiate the study of the Witten index of unitary SQCD with l ≠ 0.https://doi.org/10.1007/JHEP05(2023)148Supersymmetric Gauge TheorySupersymmetry and DualityTopological Field Theories |
| spellingShingle | Cyril Closset Osama Khlaif Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities Journal of High Energy Physics Supersymmetric Gauge Theory Supersymmetry and Duality Topological Field Theories |
| title | Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities |
| title_full | Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities |
| title_fullStr | Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities |
| title_full_unstemmed | Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities |
| title_short | Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities |
| title_sort | twisted indices bethe ideals and 3d n mathcal n 2 infrared dualities |
| topic | Supersymmetric Gauge Theory Supersymmetry and Duality Topological Field Theories |
| url | https://doi.org/10.1007/JHEP05(2023)148 |
| work_keys_str_mv | AT cyrilclosset twistedindicesbetheidealsand3dnmathcaln2infrareddualities AT osamakhlaif twistedindicesbetheidealsand3dnmathcaln2infrareddualities |