Effective String Theory and Nonlinear Lorentz Invariance

TL;DR

This paper investigates the effective action of long strings in QCD, focusing on nonlinear Lorentz invariance constraints, and identifies leading corrections to the Nambu-Goto action in various dimensions.

Contribution

It derives the form of the first allowed corrections to the Nambu-Goto action constrained by nonlinear Lorentz invariance in different spacetime dimensions.

Findings

In 2+1 dimensions, the correction is proportional to the squared curvature of the worldsheet.

In higher dimensions, the leading correction appears at a lower order than curvature squared.

The leading correction resembles the one-loop determinant computed by Polyakov for the bosonic string.

Abstract

We study the low-energy effective action governing the transverse fluctuations of a long string, such as a confining flux tube in QCD. We work in the static gauge where this action contains only the transverse excitations of the string. The static gauge action is strongly constrained by the requirement that the Lorentz symmetry, that is spontaneously broken by the long string vacuum, is nonlinearly realized on the Nambu-Goldstone bosons. One solution to the constraints (at the classical level) is the Nambu-Goto action, and the general solution contains higher derivative corrections to this. We show that in 2+1 dimensions, the first allowed correction to the Nambu-Goto action is proportional to the squared curvature of the induced metric on the worldsheet. In higher dimensions, there is a more complicated allowed correction that appears at lower order than the curvature squared. We argue that this leading correction is similar to, but not identical to, the one-loop determinant (\sqrt{-h} R \Box^{-1} R) computed by Polyakov for the bosonic fundamental string.