# Hagedorn transition In free SYM, it is known that there is a phase transition between a deconfined phase at high temperatura $T$ and a confined phase at low $T$. It is also known that it splits up into a first-order phase transition (solid line) and a third-order phase transition (dashed) when the 't Hooft coupling $\lambda$ is nonzero and small. It is conjectured that they connect to the [[0012 Hawking-Page transition|HP transition]] and Hagedorn transition, respectively, at large $\lambda$, where they can be described by holography. ![[0439_lambda_dep.png|400]] (Picture taken from Mukund Rangamani's TASI lectures.) ## Refs - original paper: [[1968#Hagedorn]] - [[1988#Atick, Witten]]: good starting point for reading <!-- rec by #ziyuewang --> - higher order corrections - [[2023#Bigazzi, Canneti, Cotrone]] and refs therein