Exact results on the Bethe Ansatz evaluation of the SCI
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913899883790336 |
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| author | Amariti, Antonio Glorioso, Pietro |
| author_facet | Amariti, Antonio Glorioso, Pietro |
| contents | We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the ones obtained by a direct evaluation of the index. The answer obtained from the BA approach using only discrete solutions for the BA equations does not always reproduce the direct evaluation result. A similar problem affects the case of $\mathrm{SU}(N)$ $\mathcal{N}=4$ SYM for $N \geq 3$, and it requires to introduce continuous solutions to the BA equations. However, we find that for $T^{1,1}$ and partially for the suspended pinch point the matching is exact in absence of the contributions from continuous solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact results on the Bethe Ansatz evaluation of the SCI Amariti, Antonio Glorioso, Pietro High Energy Physics - Theory We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the ones obtained by a direct evaluation of the index. The answer obtained from the BA approach using only discrete solutions for the BA equations does not always reproduce the direct evaluation result. A similar problem affects the case of $\mathrm{SU}(N)$ $\mathcal{N}=4$ SYM for $N \geq 3$, and it requires to introduce continuous solutions to the BA equations. However, we find that for $T^{1,1}$ and partially for the suspended pinch point the matching is exact in absence of the contributions from continuous solutions. |
| title | Exact results on the Bethe Ansatz evaluation of the SCI |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.15296 |