The ABJM Hagedorn Temperature from Integrability

TL;DR

This paper calculates the Hagedorn temperature of ABJM theory across different coupling regimes using integrability techniques, providing both numerical and analytical insights into its behavior.

Contribution

It introduces a method to compute the Hagedorn temperature in ABJM theory using the quantum spectral curve, including new results at weak and strong coupling.

Findings

Weak coupling matches known tree-level and two-loop results.

Strong coupling dependence aligns with supergravity and plane-wave limits.

Proposes an analytic form for the zero-point energy shift in string theory.

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.