Abstract
In a previous work [1], we proposed an integrability setup for computing nonplanar corrections to correlation functions in mathcal{N}=4 super-Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over graphs can be interpreted as a quantization of the string moduli space integration. The quantization requires a careful treatment of the moduli space boundaries, which is realized by subtracting degenerate Riemann surfaces; this procedure is called stratification. In this work, we precisely formulate our proposal and perform several perturbative checks. These checks require hitherto unknown multi-particle mirror contributions at one loop, which we also compute.
Highlights
Like in any perturbative string theory, closed string amplitudes in AdS5 × S5 superstring theory are given by integrations over the moduli space of Riemann surfaces of various genus
In a previous work [1], we proposed an integrability setup for computing nonplanar corrections to correlation functions in N = 4 super-Yang-Mills theory at any value of the coupling constant
Our proposal in [1] provides one realization. It can be motivated as a finite-coupling extension of a very nice proposal by Razamat [2], built up on the works of Gopakumar et al [3,4,5,6,7,8], which in turn relied on beautiful classical mathematics by Strebel [9, 10], where an isomorphism between the space of metric ribbon graphs and moduli spaces of Riemann surfaces was first understood
Summary
Like in any perturbative string theory, closed string amplitudes in AdS5 × S5 superstring theory are given by integrations over the moduli space of Riemann surfaces of various genus. Our proposal in [1] provides one realization It can be motivated as a finite-coupling extension of a very nice proposal by Razamat [2], built up on the works of Gopakumar et al [3,4,5,6,7,8], which in turn relied on beautiful classical mathematics by Strebel [9, 10], where an isomorphism between the space of metric ribbon graphs and moduli spaces of Riemann surfaces was first understood.
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