The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills

Abstract

We propose a worldsheet description for the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ string theory dual to large $N$, free $\mathcal{N}=4$ super Yang-Mills in four dimensions. The worldsheet theory is a natural generalisation 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 compelling evidence that this prescription reproduces precisely the entire planar spectrum - of single trace operators - of the free super Yang-Mills theory.

4 pages + references and supplementary material; v2: references added and small changes in wording

References in corpus (3)

• Higher Spins & Strings
• Twistor methods for AdS${}_5$
• A Note on Graviton Amplitudes for New Twistor String Theories

Cited by in corpus (4)

• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• The physical states of the Hybrid Formalism
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality