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(0,2right) 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.
Highlights
In this paper we study a model, introduced in [1], that is defined in 1+1 dimension with canonical kinetic terms and relevant SYK-like random coupling, which is a direct generalization of [55], and see [41]
We study chiral algebras in the Q-cohomology of two dimensional SYK models with extended supersymmetry
In certain limits of this family we observe emergent higher-spin symmetries in the infrared [1]. This provides an explicit illustration of a connection between SYK-like models and models with higher-spin symmetry: higher-spin theories can be thought as a subsector of some tensionless limit of string theory [56,57,58,59,60,61], while the SYK model should be holographically dual to some string theory with finite tension [7, 62]
Summary
We consider SYK models in continuous 1+1 dimensional spacetime that is of the class discussed in [55]. The coupling Jia1...aq is randomly chosen from a Gaussian distribution It is relevant, with mass dimension one, so it dominates the physics in the infrared. An intriguing feature of this model is the emergence of higher spin operators in two different limits. In each of the two limits one observes a tower of operators that become holomorphic whose left-moving conformal dimension vanish. There is a tower of antiholomorphic operators in each of the limits as well These operators close under the Operator Product Expansion (OPE) and generate a higher-spin symmetry algebra. The appearance of the higher-spin operators and higher-spin symmetry is confirmed by the vanishing of the Lyapunov exponent in the two limits. We emphasize that such higher-spin symmetries appear only in the two special limits of the IR model, which mimic the limit where the string tension approaches to zero
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
