Deformed Schur indices and Macdonald polynomials
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915184023437312 |
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| author | Hatsuda, Yasuyuki |
| author_facet | Hatsuda, Yasuyuki |
| contents | The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using Macdonald polynomials. The resulting expression is a simple combinatorial summation over partitions. An extension to line operator indices is straightforward. In particular, for an anti-symmetric representation, the line operator index has a relatively simple form. We further discuss infinite $N$ analysis and finite $N$ giant graviton expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformed Schur indices and Macdonald polynomials Hatsuda, Yasuyuki High Energy Physics - Theory Mathematical Physics The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using Macdonald polynomials. The resulting expression is a simple combinatorial summation over partitions. An extension to line operator indices is straightforward. In particular, for an anti-symmetric representation, the line operator index has a relatively simple form. We further discuss infinite $N$ analysis and finite $N$ giant graviton expansions. |
| title | Deformed Schur indices and Macdonald polynomials |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2503.03952 |