Abstract
The worldsheet string theory dual to free 4d mathcal{N} = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] 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. 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.
Highlights
What does a stringy reformulation of Yang-Mills theory look like? We have long suspected, since ’t Hooft [2], that the large N limit of gauge theories is the starting point for a dual string description
The worldsheet string theory dual to free 4d N = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 ×S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3
The sigma model we propose in [1] is a direct progeny of a similar free field sigma model proposed for the tensionless limit of AdS3 × S3 × T4 a few years ago [20]
Summary
What does a stringy reformulation of Yang-Mills theory look like? We have long suspected, since ’t Hooft [2], that the large N limit of gauge theories is the starting point for a dual string description. We have proposed a free field worldsheet sigma model that captures the tensionless (or zero radius) limit that describes free N = 4 super Yang-Mills [1]. We will show how a similar physical gauge fixing in the case of the sigma model for AdS3 × S3 gives rise to a spectrum which is a subsector of that of the dual symmetric product CFT. In some sense, it is the part of the spectrum which is independent of the compactification (e.g. to T4 or K3) of the original 10d string theory
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