N = 0 , 2 $$ \mathcal{N}=\left(0,\ 2\right) $$ SYK, chaos and higher-spins

Cheng Peng (Department of Physics, Brown University, Providence, RI, 02912, U.S.A.)

We study a 2-dimensional SYK-like model with N = 0 , 2 $$ \mathcal{N}=\left(0,\ 2\right) $$ supersymmetry. The model describes N chiral supermultiplets and M Fermi supermultiplets with a (q + 1)- field interaction. We solve the model analytically and numerically in the N ≫ 1, M ≫ 1 limit with μ M N $$ \mu \equiv \frac{M}{N} $$ being a free parameter. Two distinct higher-spin symmetries emerge when the μ parameter approaches the two ends of its range. This is verified by the appearance of conserved higher-spin operators and the vanishing of chaotic behaviors in the two limits. Therefore this model provides a manifest realization of the widely believed connection between SYK-like models and higher-spin theories. In addition, as the parameter μ varies we find the largest Lyapunov exponent of this model to be slightly larger than that in models with non-chiral supersymmetry.

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      "title": "<math> <mi>N</mi> <mo>=</mo> <mfenced> <mrow> <mn>0</mn> <mo>,</mo> <mspace width=\"0.25em\"></mspace> <mn>2</mn> </mrow> </mfenced> </math>  $$ \\mathcal{N}=\\left(0,\\ 2\\right) $$  SYK, chaos and higher-spins"
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  "abstracts": [
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      "source": "Springer", 
      "value": "We study a 2-dimensional SYK-like model with   <math> <mi>N</mi> <mo>=</mo> <mfenced> <mrow> <mn>0</mn> <mo>,</mo> <mspace width=\"0.25em\"></mspace> <mn>2</mn> </mrow> </mfenced> </math>  $$ \\mathcal{N}=\\left(0,\\ 2\\right) $$  supersymmetry. The model describes N chiral supermultiplets and M Fermi supermultiplets with a (q + 1)- field interaction. We solve the model analytically and numerically in the N \u226b 1, M \u226b 1 limit with   <math> <mi>\u03bc</mi> <mtext>\u2261</mtext> <mfrac> <mi>M</mi> <mi>N</mi> </mfrac> </math>  $$ \\mu \\equiv \\frac{M}{N} $$  being a free parameter. Two distinct higher-spin symmetries emerge when the \u03bc parameter approaches the two ends of its range. This is verified by the appearance of conserved higher-spin operators and the vanishing of chaotic behaviors in the two limits. Therefore this model provides a manifest realization of the widely believed connection between SYK-like models and higher-spin theories. In addition, as the parameter \u03bc varies we find the largest Lyapunov exponent of this model to be slightly larger than that in models with non-chiral supersymmetry."
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Published on:
14 June 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2018 (2019)
Issue 12
Pages 1-42
DOI:
https://doi.org/10.1007/JHEP12(2018)065
arXiv:
1805.09325
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: