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

TL;DR

This paper proposes 1D, N=4 supersymmetric SYK models derived from 4D supersymmetric theories, featuring fermionic and bosonic fields, with potential for random couplings and duality properties.

Contribution

It introduces a new class of 1D, N=4 supersymmetric SYK models based on compactified 4D theories, including dynamical bosons and conjectured dualities.

Findings

Models exhibit Wishart-Laguerre randomness with Gaussian couplings.

Contain dynamical bosons, aligning with other N=4 models.

Propose duality and mirror symmetry conjectures.

Abstract

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. One difference with 1D, N = 1 and N = 2 models though, is our models contain dynamical bosons, but this is consistent with other 1D, N = 4 and 2D, N = 2 models in literature. Added conjectures on duality and possible mirror symmetry realizations on these models is noted.