Finite N corrections to white hot string bits

TL;DR

This paper investigates finite N effects in string bit systems, showing that two-loop corrections to the partition function diminish as 1/N below the Hagedorn temperature, with divergences at the transition point.

Contribution

It provides the first detailed calculation of finite N corrections to the string bit partition function, revealing how divergences cancel and corrections vanish as 1/N.

Findings

Two-loop corrections vanish as 1/N below Hagedorn temperature

Divergences cancel out when summing over mode numbers

Correction coefficient diverges at the Hagedorn pole

Abstract

String bit systems exhibit a Hagedorn transition in the $N\to\infty$ limit. However, there is no phase transition when $N$ is finite (but still large). We calculate two-loop, finite $N$ corrections to the partition function in the low temperature regime. The Haar measure in the singlet-restricted partition function contributes pieces to loop corrections that diverge as $\mathcal{O}(N)$ when summed over the mode numbers. We study how these divergent pieces cancel each other out when combined. The properly normalized two loop corrections vanish as $\mathcal{O}(N^{-1})$ for all temperatures below the Hagedorn temperature. The coefficient of this $1/N$ dependence decreases with temperature and diverges at the Hagedorn pole.