A non-standard off-shell quantization of the worldsheet metric yields a self-consistent vacuum configuration and Hagedorn temperatures for confining holographic theories, reproducing known next-to-leading order and providing new partial next-to-next-to-leading order predictions.
The ABJM Hagedorn Temperature from Integrability
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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.
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Vacuum configuration of winding superstrings from non-standard semiclassical quantization
A non-standard off-shell quantization of the worldsheet metric yields a self-consistent vacuum configuration and Hagedorn temperatures for confining holographic theories, reproducing known next-to-leading order and providing new partial next-to-next-to-leading order predictions.