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

TL;DR

This paper demonstrates that the worldsheet string theory dual to free 4D ${ m extbf{N}=4}$ super Yang-Mills accurately reproduces the gauge theory spectrum, revealing a covariant, twistorial string bit structure with finite constituents.

Contribution

It shows that after gauge fixing, the worldsheet model precisely matches the spectrum of free super Yang-Mills, extending the covariant BMN string picture with a finite twistorial string bit structure.

Findings

Worldsheet theory reproduces super Yang-Mills spectrum

Spectrally flowed sectors correspond to gauge theory operators

Finite twistorial string bits form a topological worldsheet

Abstract

The worldsheet string theory dual to free 4d ${\cal N}=4$ 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 ${\rm AdS}_5\times {\rm S}^5$, and is a direct generalisation of the corresponding model for tensionless string theory on ${\rm AdS}_3\times {\rm S}^3$. As in the case of ${\rm AdS}_3$, 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.