# Strings from Feynman Diagrams

**Authors:** Rajesh Gopakumar, Rishabh Kaushik, Shota Komatsu, Edward A. Mazenc, Debmalya Sarkar  
**arXiv:** [2412.13397](https://arxiv.org/abs/2412.13397)  
**Date:** 2024-12-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2412.13397v1/

## Key points

- Manifestation of protected correlators in $\mathcal{N}=4$ Super Yang-Mills as a dual sum over closed string configurations
- Equivalence between gauge theory Feynman diagrams and dual closed string worldsheets
- $1/N$ expansion in gauge theory corresponds to genus expansion of dual closed string with $g_{st} = 1/N$
- Each Feynman diagram maps onto a specific worldsheet, indicating equivalence at individual summand level
- Weight of each Feynman diagram corresponds to exponential of Nambu-Goto action, representing area of worldsheet

## Summary

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This paper explores the manifestation of protected correlators in $\mathcal{N}=4$ Super Yang-Mills as a dual sum over closed string configurations. The Feynman diagram expansion of these correlators is recast as a sum over dual closed strings, providing a new perspective on the gauge theory. The main result, illustrated in Figure 1, shows the equivalence between the gauge theory Feynman diagrams and the dual closed string worldsheets. Three key lessons are highlighted from this duality: (1) the $1/N$ expansion in the gauge theory corresponds to the genus expansion of the dual closed string with $g_{st} = 1/N$, (2) each Feynman diagram maps precisely onto a specific worldsheet, indicating an equivalence at the level of individual summands, and (3) the weight of each Feynman diagram corresponds to the exponential of the Nambu-Goto action, representing the area of the worldsheet. The paper explains how these features arise from both a worldsheet and target space perspective. Previous work on gauge-string duality is utilized to derive this more complex example, showcasing a deeper understanding of this duality relationship. Section 2 delves into the worldsheet perspective by introducing matrix models and reviewing closed string moduli space parametrization. Section 3 shifts focus to deriving the target space picture by mapping each Feynman diagram to a holomorphic covering map. Section 4 serves as a bridge between these two perspectives, relating localization on Riemann surface moduli space to closed string configurations. The detailed plan outlined in Section 1.6 guides readers through each step of understanding this novel approach to gauge theory and string duality. Additionally, Figure 2 provides further insight by illustrating how each Feynman diagram corresponds to a specific closed string configuration. Overall, this paper offers a comprehensive exploration of how certain protected correlators in $\mathcal{N}=4$ Super Yang-Mills can be understood through a dual sum over closed string configurations. By elucidating key features and providing detailed explanations from both worldsheet and target space viewpoints, it contributes valuable insights into open/closed string duality within AdS/CFT correspondence for this topological subsector.