The ABJM Hagedorn Temperature from Integrability

Authors: Simon Ekhammar,  Joseph A. Minahan, and Charles Thull Preprint number: UUITP-16/23 Abstract: Using the quantum spectral curve we compute the Hagedorn temperature $T_H$ for ABJM theory in terms of the interpolating function $h(\lambda)$ $AdS_4$ where $\lambda=N/k$.  At weak coupling we compute $T_H$ up to eight-loop order, showing that it is consistent with 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, up to an overall factor in the shift of the zero-point energy for type IIA string theory on $AdS_4\times CP^3$.