The large-N limit of 4d superconformal indices for general BPS charges
Abstract We study the superconformal index of N $$ \mathcal{N} $$ = 1 quiver theories at large-N for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are particularly interested in the case of unequal an...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2022)013 |
| _version_ | 1797860098451701760 |
|---|---|
| author | Edoardo Colombo |
| author_facet | Edoardo Colombo |
| author_sort | Edoardo Colombo |
| collection | DOAJ |
| description | Abstract We study the superconformal index of N $$ \mathcal{N} $$ = 1 quiver theories at large-N for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are particularly interested in the case of unequal angular momenta, J 1 ≠ J 2, which has only been partially considered in the literature. We revisit the previous computation with the Bethe Ansatz formulation with generic angular momenta and extend it to encompass a large class of competing exponential terms. In the process, we also provide a simplified derivation of the original result. We consider the newly-developed elliptic extension method as well; we apply it to the J 1 ≠ J 2 case, finding a good match with the Bethe Ansatz results. We also investigate the relation between the two different approaches, finding in particular that for every saddle of the elliptic action there are corresponding terms in the Bethe Ansatz formula that match it at large-N. |
| first_indexed | 2024-04-09T21:40:21Z |
| format | Article |
| id | doaj.art-96d185dabd1d4eac81f6cabb8b3958d7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T21:40:21Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-96d185dabd1d4eac81f6cabb8b3958d72023-03-26T11:03:52ZengSpringerOpenJournal of High Energy Physics1029-84792022-12-0120221214210.1007/JHEP12(2022)013The large-N limit of 4d superconformal indices for general BPS chargesEdoardo Colombo0Dipartimento di Fisica, Università di Milano-BicoccaAbstract We study the superconformal index of N $$ \mathcal{N} $$ = 1 quiver theories at large-N for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are particularly interested in the case of unequal angular momenta, J 1 ≠ J 2, which has only been partially considered in the literature. We revisit the previous computation with the Bethe Ansatz formulation with generic angular momenta and extend it to encompass a large class of competing exponential terms. In the process, we also provide a simplified derivation of the original result. We consider the newly-developed elliptic extension method as well; we apply it to the J 1 ≠ J 2 case, finding a good match with the Bethe Ansatz results. We also investigate the relation between the two different approaches, finding in particular that for every saddle of the elliptic action there are corresponding terms in the Bethe Ansatz formula that match it at large-N.https://doi.org/10.1007/JHEP12(2022)013AdS-CFT CorrespondenceBlack Holes in String Theory |
| spellingShingle | Edoardo Colombo The large-N limit of 4d superconformal indices for general BPS charges Journal of High Energy Physics AdS-CFT Correspondence Black Holes in String Theory |
| title | The large-N limit of 4d superconformal indices for general BPS charges |
| title_full | The large-N limit of 4d superconformal indices for general BPS charges |
| title_fullStr | The large-N limit of 4d superconformal indices for general BPS charges |
| title_full_unstemmed | The large-N limit of 4d superconformal indices for general BPS charges |
| title_short | The large-N limit of 4d superconformal indices for general BPS charges |
| title_sort | large n limit of 4d superconformal indices for general bps charges |
| topic | AdS-CFT Correspondence Black Holes in String Theory |
| url | https://doi.org/10.1007/JHEP12(2022)013 |
| work_keys_str_mv | AT edoardocolombo thelargenlimitof4dsuperconformalindicesforgeneralbpscharges AT edoardocolombo largenlimitof4dsuperconformalindicesforgeneralbpscharges |