Holographic repulsion and confinement in gauge theory

TL;DR

This paper demonstrates a holographic connection between confinement in gauge theories and repulsive gravity in asymptotically anti-deSitter backgrounds, revealing a phase transition in Wilson loop behavior and a geometric signature of confinement.

Contribution

It introduces a novel interpretation of the quark-antiquark potential as affine time on null geodesics, linking confinement to holographic geometry and singularity avoidance.

Findings

Wilson loop expectation value shows Coulomb to confinement transition.

Quark-antiquark potential relates to affine time on minimal string world sheet.

Intrinsic curvature indicates confinement phase transition.

Abstract

We show that for asymptotically anti-deSitter backgrounds with negative energy, such as the AdS soliton and regulated negative mass AdS-Schwarzshild metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a Coulomb to confinement transition. We also show that the quark-antiquark ($q \bar q$) potential can be interpreted as affine time along null geodesics on the minimal string world sheet,and that its intrinsic curvature provides a signature of transition to confinement phase. The result demonstrates a UV/IR relation in that the boundary separation of the $q \bar{q}$ pair exhibits an inverse relationship with the radial descent of the world sheet into the bulk. Our results suggest a generic (holographic) relationship between confinement in gauge theory and repulsive gravity, which in turn is connected with singularity avoidance in quantum gravity.