A Worldsheet Description of Large N_c Quantum Field Theory

TL;DR

This paper develops a worldsheet theoretical framework for large N_c scalar quantum field theories, specifically for a g ext{Tr}\phi^3 interaction, linking planar diagrams to a string-like description.

Contribution

It provides the first explicit worldsheet formulation for a scalar quantum field theory in the large N_c limit, extending the conceptual connection between gauge theories and string theories.

Findings

Established a worldsheet description for scalar QFT with g ext{Tr}\u03c6^3 interaction

Demonstrated how planar Feynman diagrams correspond to a worldsheet theory

Outlined potential extensions to more complex field theories

Abstract

The N_c to infinity limit of a matrix quantum field theory is equivalent to summing only planar Feynman diagrams. The possibility of interpreting this sum as some kind world-sheet theory has been in the air ever since 't Hooft's original paper. We establish here just such a world sheet description for a scalar quantum field with interaction term g\Tr\phi^3, and we indicate how the approach might be extended to more general field theories.