A universal W-algebra for N=4 super Yang-Mills

Using bootstrap methods, we provide evidence for the existence of a non-linear W-algebra, denoted $W_{\mathrm{\infty }}^{\text{s,s}}$, which contains the small N= 4 super Virasoro algebra and features an infinite tower of additional generators, organized in short supersymmetry multiplets. The algebra $W_{\mathrm{\infty }}^{\text{s,s}}$ has one free parameter, its central charge c. We claim that the simple quotient of $W_{\mathrm{\infty }}^{\text{s,s}}$ for c= -3(N^2-1) is isomorphic to the vertex operator algebra associated to 4d N=4 $\mathfrak{s}\mathfrak{u}(N)$ super Yang-Mills theory. We define a filtration in $W_{\mathrm{\infty }}^{\text{s,s}}$ 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 $W_{\mathrm{\infty }}^{\text{s,s}}$.