Higher order corrections to the Hagedorn temperature at strong coupling

We propose a general formula for higher order corrections to the value of the Hagedorn temperature of a class of holographic confining gauge theories in the strong coupling expansion. Inspired by recent proposals in the literature, the formula combines the sigma-model string expansion with an effective approach. In particular, it includes the sigma-model contributions to the Hagedorn temperature at next-to-next-to leading order, which are computed in full generality. For NN = 4 SYM on S33 our result agrees with numerical estimates with excellent precision. We use the general formula to predict the value of the Hagedorn temperature for ABJM on S22 and for the dual of purely RR global AdS33​.