On 1D, N = 4 Supersymmetric SYK-Type Models (I)

Understand

Proposals are made to describe 1D, N = 4 supersymmetrical systems that extend SYK models by compactifying from 4D, N = 1 supersymmetric Lagrangians involving chiral, vector, and tensor supermultiplets.

• Quartic fermionic vertices are generated via integrals over the whole superspace, while 2(q-1)-point fermionic vertices are generated via superpotentials.
• The coupling constants in the superfield Lagrangians are arbitrary, and can be chosen to be Gaussian random.
• In that case, these 1D, N = 4 supersymmetric SYK models would exhibit Wishart-Laguerre randomness, which share the same feature among other 1D supersymmetric SYK models in literature.