The wall of the cave

TL;DR

This paper explores the relationship between gauge fields and string theories, proposing that Yang-Mills theories are best described by non-critical strings in a five-dimensional curved space, with implications for understanding renormalization and supersymmetry.

Contribution

It introduces new arguments for describing Yang-Mills theories with non-critical strings in five dimensions and discusses the role of the Liouville field and zigzag symmetry in this context.

Findings

Yang-Mills theories can be modeled by non-critical strings in five-dimensional curved space

The fifth dimension corresponds to the renormalization scale via the Liouville field

Presence of minimal supersymmetry on the world sheet supports zigzag symmetry

Abstract

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang Mills theories must be described by the non-critical strings in the five dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang-Mills theories. The article is written on the occasion of the 40-th anniversary of the IHES.