Twistor Coverings and Feynman Diagrams

TL;DR

This paper extends the twistor-based worldsheet duality framework from AdS3 to AdS5, linking string worldsheet covering maps to Feynman diagrams and showing the Strebel area reproduces free field propagators.

Contribution

It generalizes twistor covering maps to AdS5 and establishes their relation to Feynman diagrams via Strebel construction, providing a new geometric perspective.

Findings

Covering maps are explicitly constructed for special kinematic configurations.

The Strebel area of the worldsheet matches the free field theory propagator.

String worldsheet maps correspond to Feynman diagrams through the Strebel construction.

Abstract

Recently, a worldsheet dual to free ${\cal N}=4$ Super Yang-Mills has been proposed in terms of twistor variables for ${\rm AdS}_5$, in parallel to that for the ${\rm AdS}_3$ dual to the free symmetric orbifold CFT. In the latter case, holomorphic covering maps play a central role in determining correlators and are associated to Feynman diagrams. After recasting these maps in terms of the worldsheet twistor variables for ${\rm AdS}_3$, we generalise to ${\rm AdS}_5$. We propose stringy incidence relations and appropriate reality conditions for the twistor covering maps. For some special kinematic configurations of correlators, we exhibit an explicit construction of the corresponding covering map. We find that the closed string worldsheet corresponding to this map is related to a gauge theory Feynman diagram by the Strebel construction, as for ${\rm AdS}_3/{\rm CFT}_2$. Rather strikingly, the regularised Strebel area of the worldsheet reproduces the Feynman propagator of the free field theory.