BPS coherent states and localization
Abstract We introduce coherent states averaged over a gauge group action to study correlators of half BPS states in N $$ \mathcal{N} $$ = 4 SYM theory. The overlaps of these averaged coherent states are a generating function of correlators and can be written in terms of the Harish-Chandra-Itzykzon-Z...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2022)164 |
| _version_ | 1818000539903852544 |
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| author | David Berenstein Shannon Wang |
| author_facet | David Berenstein Shannon Wang |
| author_sort | David Berenstein |
| collection | DOAJ |
| description | Abstract We introduce coherent states averaged over a gauge group action to study correlators of half BPS states in N $$ \mathcal{N} $$ = 4 SYM theory. The overlaps of these averaged coherent states are a generating function of correlators and can be written in terms of the Harish-Chandra-Itzykzon-Zuber (HCIZ) integral. We show that this formula immediately leads to a computation of the normalization of two point functions in terms of characters obtained originally in the work of Corley, Jevicki and Ramgoolam. We also find various generalizations for A n−1 quivers that follow directly from other solvable integrals over unitary groups. All of these can be computed using localization methods. When we promote the parameters of the generating function to collective coordinates, there is a dominant saddle that controls the effective action of these coherent states in the regime where they describe single AdS giant gravitons. We also discuss how to add open strings to this formulation. These will produce calculations that rely on correlators of matrix components of unitaries in the ensemble that is determined by the HCIZ integral to determine anomalous dimensions. We also discuss how sphere giants arise from Grassman integrals, how one gets a dominant saddle and how open strings are added in that case. The fact that there is a dominant saddle helps to understand how a 1/N expansion arises for open strings. We generalize the coherent state idea to study 1/4 and 1/8 BPS states as more general integrals over unitary groups. |
| first_indexed | 2024-04-14T03:23:57Z |
| format | Article |
| id | doaj.art-9e593827dfee420197f8e5f2443f05cf |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-14T03:23:57Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9e593827dfee420197f8e5f2443f05cf2022-12-22T02:15:15ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022813610.1007/JHEP08(2022)164BPS coherent states and localizationDavid Berenstein0Shannon Wang1Department of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaAbstract We introduce coherent states averaged over a gauge group action to study correlators of half BPS states in N $$ \mathcal{N} $$ = 4 SYM theory. The overlaps of these averaged coherent states are a generating function of correlators and can be written in terms of the Harish-Chandra-Itzykzon-Zuber (HCIZ) integral. We show that this formula immediately leads to a computation of the normalization of two point functions in terms of characters obtained originally in the work of Corley, Jevicki and Ramgoolam. We also find various generalizations for A n−1 quivers that follow directly from other solvable integrals over unitary groups. All of these can be computed using localization methods. When we promote the parameters of the generating function to collective coordinates, there is a dominant saddle that controls the effective action of these coherent states in the regime where they describe single AdS giant gravitons. We also discuss how to add open strings to this formulation. These will produce calculations that rely on correlators of matrix components of unitaries in the ensemble that is determined by the HCIZ integral to determine anomalous dimensions. We also discuss how sphere giants arise from Grassman integrals, how one gets a dominant saddle and how open strings are added in that case. The fact that there is a dominant saddle helps to understand how a 1/N expansion arises for open strings. We generalize the coherent state idea to study 1/4 and 1/8 BPS states as more general integrals over unitary groups.https://doi.org/10.1007/JHEP08(2022)164AdS-CFT CorrespondenceMatrix ModelsD-Branes |
| spellingShingle | David Berenstein Shannon Wang BPS coherent states and localization Journal of High Energy Physics AdS-CFT Correspondence Matrix Models D-Branes |
| title | BPS coherent states and localization |
| title_full | BPS coherent states and localization |
| title_fullStr | BPS coherent states and localization |
| title_full_unstemmed | BPS coherent states and localization |
| title_short | BPS coherent states and localization |
| title_sort | bps coherent states and localization |
| topic | AdS-CFT Correspondence Matrix Models D-Branes |
| url | https://doi.org/10.1007/JHEP08(2022)164 |
| work_keys_str_mv | AT davidberenstein bpscoherentstatesandlocalization AT shannonwang bpscoherentstatesandlocalization |