Abstract
We study chiral algebras in the \( \overline{Q} \)-cohomology of two dimensional SYK models with extended supersymmetry. In a special limit discovered in [1], we are able to construct explicitly a “vertical” single-particle higher-spin algebra that is bilinear in the fundamental fields. This algebra can be regarded as the counterpart, when going away from criticality, of the infrared emergent higher-spin symmetry of the \( \mathcal{N}=\left(0,2\right) \) SYK model. Moreover, a second “horizontal” single-particle higher-spin algebra appears in this limit. Together with the vertical algebra they generate a stringy algebra with a “higher spin square” structure that is believed to appear in the tensionless limit of string theory. On the other hand, we do not find single-particle higher-spin algebra away from the special limit, which is consistent with the result in [1]. Our analysis is carried out for each individual realization of the random couplings and for finite N (and M), which in particular indicates that the conclusion in [1] is robust to 1/N corrections.
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ArXiv ePrint: 1812.05106
On leave from the Department of Physics, Kyungpook National University, Taegu 41566, Korea and address until August 31, 2018: C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794-3840, U.S.A. .(Changhyun Ahn)
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Ahn, C., Peng, C. Chiral algebras of two-dimensional SYK models. J. High Energ. Phys. 2019, 92 (2019). https://doi.org/10.1007/JHEP07(2019)092
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DOI: https://doi.org/10.1007/JHEP07(2019)092