$Q \bar{Q}$ Potential from Strings in Curved Spacetime - Classical Results

TL;DR

This paper derives the quark-antiquark potential using a generalized Nambu-Goto action in curved spacetime, identifying conditions for confinement and calculating string tension and potential corrections.

Contribution

It introduces a unified approach to compute the quark-antiquark potential across various curved spacetime models with an extra dimension.

Findings

Derived the condition for confinement in curved spacetime models.

Calculated the string tension in confining regimes.

Determined corrections to the linear potential.

Abstract

We compute the leading behaviour of the quark anti-quark potential from a generalized Nambu-Goto action associated with a curved space-time having an "extra dimension". The extra dimension can be the radial coordinate in the AdS/CFT correspondence, the Liouville field in Polyakov's approach, or an internal dimension in MQCD. In particular, we derive the condition for confinement, and in the case it occurs we find the string tension and the correction to the linear potential.