Extend the construction to QFTs with derivative interactions and fermions (toward gauge theories)

Extend the worldsheet construction that encodes scalar QFT Feynman rules into a string‑theoretic path integral to quantum field theories with derivative interactions and fermionic fields, thereby enabling application of the same procedure to gauge theories.

Background

The paper focuses on scalar QFTs with momentum‑independent vertices to simplify the mapping from Feynman diagrams to Riemann surfaces and the construction of a worldsheet CFT that reproduces the Feynman rules. While the authors argue there is no fundamental obstruction to generalizing the method, they do not develop the necessary extensions within the present work.

In the conclusions, the authors explicitly identify as future work the extension to more general QFTs, specifying that derivative interactions and fermions must be incorporated to apply the procedure to gauge theories. They highlight that such an extension could, for example, provide an alternative derivation of the AdS/CFT correspondence in supersymmetric gauge theories.