A universal W-algebra for N=4 super Yang-Mills
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911012393844736 |
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| author | Bonetti, Federico Meneghelli, Carlo |
| author_facet | Bonetti, Federico Meneghelli, Carlo |
| contents | Using bootstrap methods, we provide evidence for the existence of a non-linear W-algebra, denoted $W_\infty^\text{s,s}$, which contains the small N= 4 super Virasoro algebra and features an infinite tower of additional generators, organized in short supersymmetry multiplets. The algebra $W_\infty^\text{s,s}$ has one free parameter, its central charge c. We claim that the simple quotient of $W_\infty^\text{s,s}$ for c= -3(N^2-1) is isomorphic to the vertex operator algebra associated to 4d N=4 $\mathfrak{su}(N)$ super Yang-Mills theory. We define a filtration in $W_\infty^\text{s,s}$ and provide evidence that it reproduces the R-filtration, which is crucial to extract 4d SCFT data from the vertex operator algebra. Finally, we present explicit formulae for all the (anti)commutators of the wedge algebra of $ W_\infty^\text{s,s}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A universal W-algebra for N=4 super Yang-Mills Bonetti, Federico Meneghelli, Carlo High Energy Physics - Theory Using bootstrap methods, we provide evidence for the existence of a non-linear W-algebra, denoted $W_\infty^\text{s,s}$, which contains the small N= 4 super Virasoro algebra and features an infinite tower of additional generators, organized in short supersymmetry multiplets. The algebra $W_\infty^\text{s,s}$ has one free parameter, its central charge c. We claim that the simple quotient of $W_\infty^\text{s,s}$ for c= -3(N^2-1) is isomorphic to the vertex operator algebra associated to 4d N=4 $\mathfrak{su}(N)$ super Yang-Mills theory. We define a filtration in $W_\infty^\text{s,s}$ and provide evidence that it reproduces the R-filtration, which is crucial to extract 4d SCFT data from the vertex operator algebra. Finally, we present explicit formulae for all the (anti)commutators of the wedge algebra of $ W_\infty^\text{s,s}$. |
| title | A universal W-algebra for N=4 super Yang-Mills |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.15678 |