A supersymmetric SYK model with a curious low energy behavior

Abstract

We consider $\mathcal{N}$ = 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like $S=S_0+\text{(constant)}{T}^a$, where $a\ne 1$. The large $N$ equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.

v2: minor changes

References in corpus (17)

• Comments on the Sachdev-Ye-Kitaev model
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Aspects of holography for theories with hyperscaling violation
• The Number of Eigenvalues of a Tensor
• More on Supersymmetric and 2d Analogs of the SYK Model
• Disordered Quivers and Cold Horizons
• The Quantum Spherical p-Spin-Glass Model
• Black hole entropy from non-perturbative gauge theory
• Approximations for strongly-coupled supersymmetric quantum mechanics
• Quantum TAP equations
• Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs
• Comments on thermodynamics of supersymmetric matrix models
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Melonic dominance and the largest eigenvalue of a large random tensor
• Exact analytic expressions of real tensor eigenvalue distributions of Gaussian tensor model for small $N$
• Generalized Euler Index, Holonomy Saddles, and Wall-Crossing

Cited by in corpus (5)

• D-commuting SYK model: building quantum chaos from integrable blocks
• $\mathcal{N}=2$ SYK models with dynamical bosons and fermions
• KdV conformal symmetry breaking in nearly AdS${}_2$
• Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape
• Off-diagonal coupling of supersymmetric SYK model