A Study of confinement for $Q\bar{Q}$ potentials on D3, M2 & M5 branes

TL;DR

This paper analyzes quark-antiquark interaction potentials on D3, M2, and M5 branes, revealing confining and non-confining behaviors depending on proximity to the horizon, aligning with expectations from conformal and non-conformal field theories.

Contribution

It provides a comparative study of confinement phenomena in different brane backgrounds using Wilson loops, highlighting the transition between confining and non-confining regimes.

Findings

Near horizon potentials are non-confining, matching conformal field theory.

Far from horizon, potentials exhibit confinement, similar to QCD flux tubes.

Transition between regimes varies across D3, M2, and M5 brane scenarios.

Abstract

We study analytically and numerically the interaction potentials between a pair of quark an anti-quark on D3, M2 and M5 branes. These potentials are obtained using Maldacena's method involving Wilson loops and present confining and non-confining behaviours in different situations that we explore in this work. In particular, at the near horizon geometry the potentials are non-confining in agreement with conformal field theory expectations. On the other side, far from horizon, the dual field theories are no longer conformal and the potentials present confinement. This is in agreement with the behaviour of strings in flat space where the string mimics the expected flux tube of QCD. A study of the transition between the confining/non-confining regimes in the three different scenarios (D3, M2, M5) is also performed.