The wall of the cave

TL;DR

The paper argues that Yang-Mills theories can be described by non-critical strings in a curved five-dimensional space, with the Liouville field $\varphi$ acting as the renormalization scale. It develops a framework where conformal invariance and zigzag symmetry constrain boundary states to vector (gluon) modes, and shows that worldsheet supersymmetry with a non-chiral GSO projection can remove boundary tachyons, enabling a bosonic YM interpretation. It surveys constant-curvature backgrounds such as $L_5×S^5$ and $AdS_5×S^5$-like near-brane geometries, exploring conditions for conformal fixed points or asymptotic freedom depending on RR-fields and dilaton profiles. Together, these insights outline a plausible gauge–string correspondence in a non-critical, higher-dimensional setting and motivate seeking exact CFT realizations with potential implications for YM dynamics.

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.