Strings from Logic

TL;DR

This paper explores the idea that strings could be purely mathematical entities derived from logical axioms, linking logical proofs to string theories via large-N field theories and Feynman diagrams.

Contribution

It introduces a novel framework connecting logical proofs with string theories through large-N field theories and Feynman diagrams, suggesting a new perspective on the nature of strings and undecidable theorems.

Findings

Proof graphs can be interpreted as Feynman diagrams.

Large-N theories are dual to string theories.

Undecidable theorems may relate to nonperturbative effects.

Abstract

What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom. Strings arise, because these large-N theories are dual to string theories. These ``logical quantum field theories'' map theorems into the space of functions of two parameters: N and the coupling constant. Undecidable theorems might be related to nonperturbative field theory effects.