The Worldsheet Dual of Free Super Yang-Mills in 4D

Abstract

The worldsheet string theory dual to free 4d $\mathcal{N}=4$ super Yang-Mills theory was recently proposed in arXiv:2104.08263. It is described by a free field sigma model on the twistor space of ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$, and is a direct generalisation of the corresponding model for tensionless string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3$. As in the case of ${\mathrm{AdS}}_3$, the worldsheet theory contains spectrally flowed representations. We proposed in arXiv:2104.08263 that in each such sector only a finite set of generalised zero modes (`wedge modes') are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. More specifically, the states in the sector with $w$ units of spectral flow match with single trace operators built out of $w$ super Yang-Mills fields (`letters'). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet.

arXiv comment50 pages

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• Perturbing the symmetric orbifold from the worldsheet
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• Disordered vector models: from higher spins to incipient strings
• DDF operators in the Hybrid Formalism
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• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality