Higher order corrections to the Hagedorn temperature at strong coupling
Francesco Bigazzi, Tommaso Canneti, Aldo L. Cotrone
Abstract
A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM on S 3 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 S 2 and for the dual of purely RR global AdS 3 .