Wilson Loops for M2- and M5-brane spaces

TL;DR

This paper computes energies of string-like membranes in M2- and M5-brane backgrounds, exploring their dual gauge theories via AdS/CFT, revealing confinement and non-confinement potentials in different regimes.

Contribution

It provides new calculations of membrane configurations in M-brane backgrounds, connecting these to quark interactions in dual gauge theories, including confinement behavior.

Findings

Near horizon energies match dual gauge theory predictions.

Identified regimes with confining and non-confining potentials.

Calculated energies far from the horizon in complex backgrounds.

Abstract

We calculate configuration energies of string-like membranes in M2- and M5-brane spaces. In the near horizon approximation these backgrounds reduce to $AdS_4\times S^7$ and $AdS_7\times S^4$ spaces and the dual theories are supersymmetric $SU(N)$ gauge theories, in accordance with the AdS/CFT correspondence. In this case the string-like configuration energy is identified with the quark and anti-quark energy interaction in the dual theories. Far from the horizon the dual theory is more involved but any how we were able to calculate the string-like configuration energy. For limiting regimes we find simpler solutions for which some potentials exhibit a confinement behavior while others are non-confining.