Finite N corrections to white hot string bits

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.

arXiv commentadded references, modified certain passages

References in corpus (10)

• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• Reformulating String Theory with the $1/N$ Expansion
• String Bit Models for Superstring
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Space from String Bits
• String Bits at Finite Temperature and the Hagedorn Phase
• Hagedorn Temperature in Superstring Bits and SU(N) Characters
• Color Characters for White Hot String Bits
• Thermal properties of a string bit model at large N

Cited by in corpus (1)

• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$