Static strings in Randall-Sundrum scenarios and the quark anti-quark potential

TL;DR

This paper investigates static string energies in an AdS slice with branes, revealing a potential that resembles the quark-antiquark interaction in confining gauge theories, and suggests a duality with such theories.

Contribution

It introduces a model of static strings in an AdS slice with branes, deriving a potential analogous to the Cornell potential, and proposes a duality with confining gauge theories.

Findings

Energy grows linearly with separation at large distances.

Energy exhibits Coulomb-like behavior at short distances.

Identifies parameters matching the Cornell potential.

Abstract

We calculate the energy of a static string in an AdS slice between two D3-branes with orbifold condition. The energy for configurations with endpoints on a brane grows linearly for large separation between these points. The derivative of the energy has a discontinuity at some critical separation. Choosing a particular position for one of the branes we find configurations with smooth energy. In the limit where the other brane goes to infinity the energy has a Coulombian behaviour for short separations and can be identified with the Cornell potential for a quark anti-quark pair. This identification leads to effective values for the AdS radius, the string tension and the position of the infrared brane. These results suggest an approximate duality between static strings in an AdS slice and a heavy quark anti-quark configuration in a confining gauge theory.