Hagedorn Behaviour of Little String Theory from String Corrections to NS5-Branes

TL;DR

This work tests the near-horizon NS5-brane / Little String Theory duality by incorporating string corrections into NS5-brane thermodynamics. It shows that tree-level temperature corrections vanish due to the exact CFT description, while the leading one-loop correction yields a nontrivial temperature dependence $T = T_{\rm hg} \left( 1 - \frac{\pi^2 b}{2} \frac{1}{N^2 l_s^2 u_0^2} \right)$, producing an entropy $S(T) = k \frac{T_{\rm hg}}{T_{\rm hg}-T}$ with $k = \pi^3 b N \hat{V}_5$ and, equivalently, $S(E) = \beta_{\rm hg} E + k \log E$. The results align with the statistical thermodynamics of a 5+1D closed string theory, supporting the duality and showing that $T_{\rm hg}$ acts as a limiting temperature. Higher-loop corrections organize into a consistent expansion, and the analysis yields a concrete prediction for the constant $k$ while pointing to further extensions to heterotic and non-commutative LST cases.

Abstract

Following the conjectured duality between near-horizon NS5-branes and little string theory, the string-corrected thermodynamics of near-horizon NS5-branes is studied and found to agree with the statistical thermodynamics of a 5+1 dimensional supersymmetric string theory near the Hagedorn temperature. Specifically, tree-level corrections to the temperature are argued to vanish, in accordance with the duality, while the one-loop string correction to the NS5-brane thermodynamics is shown to generate the correct temperature dependence of the entropy.