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${}_4\times \mathbb{C}{\text{P}}^3$. We conjecture an analytic form for this shift to leading order that is consistent with our numerical results.

19 pages, 5 figures, 2 ancillary files. V2: references added, typos corrected, updated numerical data