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Supersymmetric SYK models
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abstract
We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The ${\cal N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$. We also compute the large $N$ spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an ${\cal N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.
Forward citations
Cited by 9 Pith papers
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Extended JT supergravity and random matrix models: The power of the string equation
The string equation, with simple analyticity requirements, determines BPS sectors from non-BPS sectors and yields matrix model descriptions for N=3 and large N=4 JT supergravity.
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Thermal two-point functions in SYK and complex-time singularities
The large-N SYK thermal two-point function exhibits complex-time singularities—an effective-temperature pole and a subleading bouncing-geodesic-like singularity—that persist from infinite to zero temperature.
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$E$ and $J$ type $\mathcal{N}=(0,2)$ disordered models and higher-spin symmetry
The E-type N=(0,2) disordered model is dynamically equivalent to the J-type model in the IR, inheriting its emergent higher-spin symmetry.
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Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model
In double-scaled complex SYK, grand-canonical Krylov complexity is the charge-weighted sum of canonical complexities, saturating a conjectured inequality.
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Krylov Complexity of Supersymmetric SYK Models
In finite-size N=2 SYK, breaking supersymmetry with an irrelevant deformation pushes late-time Krylov complexity to roughly half the maximal Krylov-space bound, while a mass deformation leaves saturation complexity a ...
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A generalized latent-entropy measure orders k-uniform states, maxes out on AME states, shows odd-party random states saturate it, and distinguishes SYK variants.
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A folded string dual for the Sachdev-Ye-Kitaev model
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Entanglement production in the Sachdev-Ye-Kitaev Model and its variants
Entanglement production rates distinguish the spin-SYK model from fermionic SYK and binary SYK, and the differences only become visible at larger system sizes.
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The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
The paper attributes the cuprate 'foot' to a disordered spin-density-wave transition and the 'fan' to a disorder-tuned FL-to-FL* Fermi-volume-changing transition described by a two-dimensional Yukawa-SYK model.
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