The ABJM Hagedorn Temperature from Integrability

Abstract

We use the quantum spectral curve to compute the Hagedorn temperature for ABJM theory in terms of the interpolating function $h(\lambda)$. At weak coupling we compute this temperature up to eight-loop order, showing that it matches the known tree-level and two-loop results. At strong coupling we compute the dependence numerically, showing that it is consistent with expectations from supergravity and the plane-wave limit for the four leading terms in the strong coupling expansion, up to an overall shift of the zero-point energy for type IIA string theory on AdS$_4\times \mathbb{C}\textrm{P}^3$. We conjecture an analytic form for this shift to leading order that is consistent with our numerical results.