Non-planar integrated correlator in $\mathcal{N}=4$ SYM
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916443838218240 |
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| author | Zhang, Shun-Qing |
| author_facet | Zhang, Shun-Qing |
| contents | Integrated correlator of four superconformal stress-tensor primaries in $SU(N)$ $\mathcal{N}=4$ super Yang-Mills (SYM) theory in the perturbative limit takes a remarkably simple form, where the $L$-loop coefficient is given by a rational multiple of $ζ(2L+1)$. In this letter, we extend the previous analysis of expressing the perturbative integrated correlator as a linear combination of periods of $f$-graphs, graphical representations for loop integrands, to the non-planar sector at four loops. At this loop order, multiple zeta values make their first appearance when evaluating periods of non-planar $f$-graphs, but cancel non-trivially in the weighted sum. The remaining single zeta value, along with the rational number prefactor, makes a perfect agreement with the prediction from supersymmmetric localisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-planar integrated correlator in $\mathcal{N}=4$ SYM Zhang, Shun-Qing High Energy Physics - Theory Integrated correlator of four superconformal stress-tensor primaries in $SU(N)$ $\mathcal{N}=4$ super Yang-Mills (SYM) theory in the perturbative limit takes a remarkably simple form, where the $L$-loop coefficient is given by a rational multiple of $ζ(2L+1)$. In this letter, we extend the previous analysis of expressing the perturbative integrated correlator as a linear combination of periods of $f$-graphs, graphical representations for loop integrands, to the non-planar sector at four loops. At this loop order, multiple zeta values make their first appearance when evaluating periods of non-planar $f$-graphs, but cancel non-trivially in the weighted sum. The remaining single zeta value, along with the rational number prefactor, makes a perfect agreement with the prediction from supersymmmetric localisation. |
| title | Non-planar integrated correlator in $\mathcal{N}=4$ SYM |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.18900 |