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.

arXiv comment4 pages + references and supplementary material; v2: references added and small changes in wording

References in corpus (33)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Review of AdS/CFT Integrability: An Overview
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• Foundations of the AdS_5 x S^5 Superstring. Part I
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Ambitwistor strings and the scattering equations
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• The Worldsheet Dual of the Symmetric Product CFT
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Gauge Fields and Space-Time
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Higher Spins & Strings
• On stringy AdS_5 x S^5 and higher spin holography
• Higher Spin Symmetry and N=4 SYM
• Free Large N Supersymmetric Yang-Mills Theory as a String Theory
• Covariant Quantization of the Green-Schwarz Superstring in a Calabi-Yau Background
• From Free Fields to $AdS$ -- III
• On the spectrum of AdS/CFT beyond supergravity
• On the Uniqueness of String Theory
• Free field world-sheet correlators for ${\mathrm{AdS}}_3$
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• Towards a string bit formulation of N=4 super Yang-Mills
• Tree and Loop Amplitudes in Open Twistor String Theory
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• Twistor methods for AdS${}_5$
• On a worldsheet dual of the Gaussian matrix model
• A Note on Graviton Amplitudes for New Twistor String Theories
• Superstrings from theories with N>1 world-sheet supersymmetry
• UNIVERSAL STRING AND SMALL $N=4$ SUPERSTRING

Cited by in corpus (26)

• Holographic spacetime, black holes and quantum error correcting codes: A review
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• Exact Stringy Microstates from Gauge Theories
• Decoding stringy near-supersymmetric black holes
• Perturbing the symmetric orbifold from the worldsheet
• Chiral Higher Spin Gravity and Convex Geometry
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• The free field realisation of the BVW string
• Disordered vector models: from higher spins to incipient strings
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• DDF operators in the Hybrid Formalism
• Twistor Coverings and Feynman Diagrams
• Giant gravitons in twisted holography
• Field theory expansions of string theory amplitudes
• Infinite distances in multicritical CFTs and higher-spin holography
• Classical geometry from the tensionless string
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• A Celestial Route to AdS Bulk Locality
• The physical states of the Hybrid Formalism
• Worldsheet Free Fields, Higher Spin Symmetry and Free $\mathcal{N}=4$ Super Yang-Mills
• String theory in twistor space and minimal tension holography
• Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• Structure of the $\mathcal{N}=4$ chiral algebra
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality