Localized states of BFSS super quantum mechanics

Abstract

We analyze the recently discovered localized and non-uniform phases of the Banks-Fischler-Shenker-Susskind (BFSS) matrix quantum mechanics. Building on [1], we provide first-principles derivations of their properties and extend the results with new analytic and numerical insights. We show that strongly coupled BFSS dynamics emerge from a specific Carrollian transformation of 11-dimensional supergravity, which we justify in detail. In this framework, the uniform BFSS phase corresponds to a black string in a pp-wave background. We demonstrate that this background is unstable to a Gregory Laflamme instability and, for the first time, compute the associated growth rate. The instability gives rise to non-uniform and localized phases that dominate the microcanonical ensemble in certain low-energy regimes, with the localized phase also prevailing in the canonical ensemble at low temperatures. We identify the corresponding first- and second order phase transitions and derive analytic formulas for the thermodynamics of the localized phase, accurate to better than 0.3% against numerical results.

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ORCID for Oscar J.C. Dias: orcid.org/0000-0003-4855-4750

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