QCD String as an Effective String

TL;DR

This paper explores the effective string description of QCD strings, solving the static potential in the mean-field approximation and addressing tachyonic instabilities by incorporating extrinsic curvature terms.

Contribution

It demonstrates the exact solvability of the static potential for the Nambu-Goto string and proposes a method to cure tachyonic instabilities using extrinsic curvature operators.

Findings

Mean-field approximation yields exact static potential for Nambu-Goto string.

Adding extrinsic curvature operators removes tachyonic instabilities.

Effective string theory describes QCD strings in specific regimes.

Abstract

There are two cases where QCD string is described by an effective theory of long strings: the static potential and meson scattering amplitudes in the Regge regime. I show how the former can be solved in the mean-field approximation, justified by the large number of space-time dimensions, and argue that it turns out to be exact for the Nambu--Goto string. By adding extrinsic curvature I demonstrate how the tachyonic instability of the ground-state energy can be cured by operators less relevant in the infrared.