What is the Simplest Gauge-String Duality?

Abstract

We make a proposal for the string dual to the simplest large $N$ theory, the Gaussian matrix integral in the 'tHooft limit, and how this dual description emerges from double line graphs. This is a specific realisation of the general approach to gauge-string duality which associates worldsheet riemann surfaces to the Feynman-'tHooft diagrams of a large N gauge theory. We show that a particular version (proposed by Razamat) of this connection, involving integer Strebel differentials, naturally explains the combinatorics of Gaussian matrix correlators. We find that the correlators can be explicitly realised as a sum over a special class of holomorphic maps (Belyi maps) from the worldsheet to a {\it target space} ${\mathbb{P}}^1$. We are led to identify this target space with the riemann surface associated with the (eigenvalues of the) matrix model. In the process, an AdS/CFT like dictionary, for arbitrary correlators of single trace operators, also emerges in which the holomorphic maps play the role of stringy Witten diagrams. Finally, we provide some evidence that the above string dual is the conventional A-model topological string theory on ${\mathbb{P}}^1$.

30+1 pages, 6 figures

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• Strings from Feynman Graph counting : without large N
• Correlators in the Simplest Gauge-String Duality
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• On the refined counting of graphs on surfaces
• Holography as a highly efficient RG flow I: Rephrasing gravity
• Giant gravitons in twisted holography
• Topological String Correlators from Matrix Models
• Permutation combinatorics of worldsheet moduli space
• Holographic Hierarchy in the Gaussian Matrix Model via the Fuzzy Sphere
• Hidden symmetries and Large N factorisation for permutation invariant matrix observables
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• Symmetric Group Gauge Theories and Simple Gauge/String Dualities
• Multi-trace Correlators from Permutations as Moduli Space