Multi-matrix correlators and localization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916109547995136 |
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| author | Holguin, Adolfo Wang, Shannon Wang, Zi-Yue |
| author_facet | Holguin, Adolfo Wang, Shannon Wang, Zi-Yue |
| contents | We study generating functions of $\frac{1}{4}$-BPS states in $\mathcal{N}=4$ super Yang-Mills at finite $N$ by attempting to generalize the Harish-Chandra-Itzykson-Zuber integral to multiple commuting matrices. This allows us to compute the overlaps of two or more generating functions; such calculations arise in the computation of two-point correlators in the free-field limit. We discuss the four-matrix HCIZ integral in the $U(2)$ context and lay out a prescription for finding a more general formula for $N>2$. We then discuss its connections with the restricted Schur polynomial operator basis. Our results generalize readily to arbitrary numbers of matrices, opening up the opportunity to study more generic BPS operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03235 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-matrix correlators and localization Holguin, Adolfo Wang, Shannon Wang, Zi-Yue High Energy Physics - Theory We study generating functions of $\frac{1}{4}$-BPS states in $\mathcal{N}=4$ super Yang-Mills at finite $N$ by attempting to generalize the Harish-Chandra-Itzykson-Zuber integral to multiple commuting matrices. This allows us to compute the overlaps of two or more generating functions; such calculations arise in the computation of two-point correlators in the free-field limit. We discuss the four-matrix HCIZ integral in the $U(2)$ context and lay out a prescription for finding a more general formula for $N>2$. We then discuss its connections with the restricted Schur polynomial operator basis. Our results generalize readily to arbitrary numbers of matrices, opening up the opportunity to study more generic BPS operators. |
| title | Multi-matrix correlators and localization |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2307.03235 |