High Temperature Partition Function of the Rigid String

TL;DR

This paper compares the high temperature free energy of the rigid string to the QCD string, highlighting differences in phase and sign, and discusses the implications for string theory models of QCD.

Contribution

It provides an analysis of the high temperature behavior of the rigid string and its relation to the QCD string, emphasizing the limitations of the rigid string model.

Findings

High temperature free energy of rigid string matches QCD string dimensionally

Sign and phase differences suggest rigid string may not fully describe QCD

Fourth derivative action complicates the rigid string's validity as a model

Abstract

We find that the high temperature limit of the free energy per unit length for the rigid string agrees dimensionally with that of the QCD string (unlike the Nambu-Goto string). The sign, and in fact the phase, do not agree. While this may be a clue to a string theory of QCD, we note that the problem of the fourth derivative action makes it impossible for the rigid string to be a correct description.