Strings from Feynman Diagrams

TL;DR

This paper demonstrates how Feynman diagrams in a specific supersymmetric gauge theory can be interpreted as discrete points on string moduli space, revealing a microscopic open/closed string duality and multiple open string descriptions within the AdS/CFT framework.

Contribution

It provides a detailed mapping of gauge theory Feynman diagrams to Riemann surfaces, illustrating string emergence from matrix models and uncovering multiple open string duals for the same closed string theory.

Findings

Feynman diagrams correspond to points on string moduli space.

Multiple open string descriptions can encode the same closed string theory.

The mapping is realized at the level of a two-matrix integral.

Abstract

For correlators in $\mathcal{N}=4$ Super Yang-Mills preserving half the supersymmetry, we manifestly recast the gauge theory Feynman diagram expansion as a sum over dual closed strings. Each individual Feynman diagram maps on to a Riemann surface with specific moduli. The Feynman diagrams thus correspond to discrete lattice points on string moduli space, rather than discretized worldsheets. This picture is valid to all orders in the $1/N$ expansion. Concretely, the mapping is carried out at the level of a two-matrix integral with its dual string description. It provides a microscopic picture of open/closed string duality for this topological subsector of the full AdS/CFT correspondence. At the same time, the concrete mechanism for how strings emerge from the matrix model Feynman diagrams predicts that multiple open string descriptions can exist for the same dual closed string theory. By considering the insertion of determinant operators in $\mathcal{N}=4$ SYM, we indeed find six equivalent open-string descriptions. Each of them generates Feynman diagrams related to one another via (partial) graph duality, and hence encodes the same information. The embedding of these Kontsevich-like duals into the 1/2 SUSY sector of AdS/CFT is achieved by open strings on giant graviton branes.