On the applicability of holography in thermodynamic equilibrium

Abstract

For a strongly coupled system that has a gravity dual description, we show that the standard holographic dictionary yields a nonnegative susceptibility when the system is in thermodynamic equilibrium and the correlation function is absolutely integrable. When the system has no spontaneous condensation or has a spontaneous ${\mathbb{Z}}_2$-symmetry breaking, we find that the ``trace energy condition" is violated in many cases. There is a normalized grand potential density that is monotonic as accessing to lower scales, providing a candidate $c$-function characterizing the number of effective degrees of freedom. Finally, we discuss a ``paradox'' raising by the negative susceptibility in holography and its resolution.

The published version

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