String Dual to Free $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory

We propose a worldsheet description for the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ string theory dual to large $N$, free $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four dimensions. The worldsheet theory is a natural generalization of the recently investigated tensionless string on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathbb{T}}^4$. As in the case of ${\mathrm{AdS}}_3$ it has a free field description, with spectrally flowed sectors, and is closely related to an (ambi-)twistor string theory. Here, however, we view it as a critical $N=4$ (closed) string background. We argue that the corresponding worldsheet gauge constraints reduce the degrees of freedom to a finite number of oscillators (string bits) in each spectrally flowed sector. Imposing a set of residual gauge constraints on this reduced oscillator Fock space then determines the physical spectrum of the string theory. Quite remarkably, we find that this prescription reproduces precisely the entire planar spectrum—of single trace operators—of the free supersymmetric Yang-Mills theory.