Aspects of the D0 brane black hole and a SUSY SYK model

<!--HTML--><p style="-webkit-text-stroke-width:0px;caret-color:rgb(29, 29, 29);color:rgb(29, 29, 29);font-family:Calibri;font-size:16px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:auto;text-align:start;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;widows:auto;word-spacing:0px;">I will discuss the black hole solution dual to the BFSS matrix model in the 't Hooft limit. The classical physics of this black hole is invariant under a scale transformation, or ``similarity,'' that changes the action by an overall multiplicative factor, and is related to the peculiar temperature dependence of the entropy, $S \propto T^{9/5}$. The similarity fixes the masses of fluctuations around this background. This fact, as well as a mathematical trick where we view the solution as the dimensional reduction of an $AdS_{2 + 9/5} \times S^{8}$ geometry, allows for a simple computation of the black hole quasinormal modes.</p><p style="-webkit-text-stroke-width:0px;caret-color:rgb(29, 29, 29);color:rgb(29, 29, 29);font-family:Calibri;font-size:16px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:auto;text-align:start;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;widows:auto;word-spacing:0px;">I will then discuss an $\mathcal{N} = 2$ supersymmetric SYK model. The large $N$ equations for this model are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing BFSS. This model has a peculiar low energy behavior in which the scalar fields develop large expectation values. In contrast to BFSS, it is found to have a ground state entropy and appears sub-maximally chaotic at low temperatures. While the initial motivation to study the model was based on similarities with BFSS, the physics looks fairly different.</p><p style="-webkit-text-stroke-width:0px;caret-color:rgb(29, 29, 29);color:rgb(29, 29, 29);font-family:Calibri;font-size:16px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:auto;text-align:start;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;widows:auto;word-spacing:0px;"><span style="background-color:rgb(255,255,255);color:rgb(29,29,29);"><span style="-webkit-text-stroke-width:0px;caret-color:rgb(29, 29, 29);display:inline !important;float:none;font-family:Calibri;font-size:16px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:auto;text-align:start;text-decoration:none;text-indent:0px;text-transform:none;white-space:normal;widows:auto;word-spacing:0px;">Based on arXiv:2303.09974, arXiv:2309.08818.</span></span></p>