Yang-Mills theory from non-critical string

TL;DR

This paper explores the connection between non-critical string theory and Yang-Mills theory, identifying solutions that exhibit key features like asymptotic freedom and the area law for Wilson loops, near fixed points.

Contribution

It proposes two solutions to bulk equations in non-critical string theory that correspond to different regimes of Yang-Mills theory, highlighting their physical behaviors.

Findings

One solution approaches AdS space at UV, realizing conformal invariance.

The other approaches flat space in both IR and UV, showing confinement.

Wilson loop area law and asymptotic freedom are demonstrated.

Abstract

The correspondence of the non-critical string theory and the Yang-Mills theory is examined according to the recent Polyakov's proposal, and two possible solutions of the bulk equations are addressed near the fixed points of the pure Yang-Mills theory: (i) One solution asymptotically approaches to the AdS space at the ultraviolet limit where the conformally invariant field theory is realized. (ii) The second one approaches to the flat space in both the infrared and the ultraviolet limits. The area law of the Wilson-loop and the asymptotic freedom with logarithmic behaviour are seen in the respective limit.