A Study of Confinement for QQ- Potentials on D3, M2, and M5 Branes

Edward Quijada,Henrique Boschi-Filho

doi:10.1155/2017/6124619

Abstract

We study analytically and numerically the interaction potentials between a pair of quark and antiquark on D3, M2, and M5 branes. These potentials are obtained using Maldacena’s method involving Wilson loops and present confining and nonconfining behaviours in different situations that we explore in this work. In particular, at the near horizon geometry, the potentials are nonconfining 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/nonconfining regimes in the three different scenarios (D3, M2, and M5) is also performed.

Highlights

In quantum field theory, the Wilson loop operator is defined as where C denotes a closed loop in space-time and the trace is over the fundamental representation of the gauge field A with SU(N) symmetry
It is important to remark that this is not a thermal phase transition since we are working at zero temperature and the transition is of geometrical nature
We presented an analysis of the Wilson loop for the D3 brane background

Summary

Introduction

Where C denotes a closed loop in space-time and the trace is over the fundamental representation of the gauge field A with SU(N) symmetry. The expectation value of the Wilson loop is related to the worldsheet area S of a string whose boundary is the loop in question such that Maldacena used this approach to calculate the quarkantiquark potential for the string in the AdS5 ×S5 background [6] obtaining a nonconfining potential for the infinitely massive quark-antiquark pair, consistent with the conformal symmetry of the dual super Yang-Mills theory. We are able to work with string-like objects and to the case of strings on D3 backgrounds, and we utilize the static configuration and the MRY proposal to get the distance separation and energy interaction between a pair of quarkantiquark on M2 (M5) branes (see [23])

D3 Brane

M2 Brane

M5 Brane

Discussions and Conclusion