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

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.