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It is expected that the Gregory-Laflamme (GL) instability in the black stringin gravity is related to the Rayleigh-Plateau instability in fluid mechanics.Especially, the orders of the phase transitions associated with theseinstabilities depend on the number of the transverse space dimensions, and theyare of first and second order below and above the critical dimension. Throughthe gauge-gravity correspondence, the GL instability is conjectured to bethermodynamically related to the Hagedorn instability in large-N gaugetheories, and it leads to a prediction that the order of theconfinement-deconfinement transition associated with the Hagedorn instabilitymay depend on the transverse dimension. We test this conjecture in theD-dimensional bosonic D0-brane model using numerical simulation and the 1/Dexpansion, and confirm the expected D dependence.

Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities