Abstract
We study the Schwinger-Dyson equations of a fermionic planar matrix quantum mechanics [or tensor and Sachdev-Ye-Kitaev (SYK) models] at leading melonic order. We find two solutions describing a high entropy, SYK black-hole-like phase and a low entropy one with trivial IR behavior. There is a line of first order phase transitions that terminates at a new critical point. Critical exponents are nonmean field and differ on the two sides of the transition. Interesting phenomena are also found in unstable and stable bosonic models, including Kazakov critical points and inconsistency of SYK-like solutions of the IR limit.
Highlights
It is straightforward to write down the SD equations and check that they have the following properties: (i) They have no real solution in a large strongly coupled region of the ðm; TÞ plane, shaded in gray in Fig. 5 and bounded by an instability curve. (ii) To the right of the instability curve, the SD equations have two real solutions
In this Letter, we focus on the discussion of the physics and on the presentation of the main results
A remarkable property of fermionic models like (1) is that there are two natural but distinct ways to define a perturbative expansion and a priori two distinct paths to access the nonperturbative physics using the strategy described in the previous paragraph
Summary
After taking the usual planar N → ∞ limit, we are considering the new D → ∞ limit at fixed λ defined in [4]. We first start from perturbation theory to compute physical quantities as a power expansion in the coupling constant λ in terms of Feynman graphs. We consider the large N and large D limits, which in our case, select the planar melonic graphs described in [4] This truncation of perturbation theory produces a convergent series expansion. A remarkable property of fermionic models like (1) is that there are two natural but distinct ways to define a perturbative expansion and a priori two distinct paths to access the nonperturbative physics using the strategy described in the previous paragraph. The system is in the unique Fock vacuum state and obviously has zero entropy This remains true after perturbation theory is resummed. The qualitative difference between the two perturbative expansions comes from the fact that the T → 0 and m → 0 limits of Gð0Þ do not commute; depending on the order of the limits, one obtains either the zero temperature
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