Towards a 2d QFT Analog of the SYK Model

TL;DR

This paper introduces a two-dimensional quantum field theory model that generalizes the SYK model, exhibiting conformal symmetry, emergent modes, and connections to gravity and deformations, advancing understanding of holographic dualities.

Contribution

It presents a novel 2D QFT model extending the SYK framework, linking IR dynamics to gravity and deformations, and exploring its topological and conformal properties.

Findings

Model preserves key features of the SYK model.

Emergent pseudo-Goldstone mode matches 3D AdS gravity action.

Spectral density deviations resemble a T T̄ deformation.

Abstract

We propose a 2D QFT generalization of the Sachdev-Ye-Kitaev model, which we argue preserves most of its features. The UV limit of the model is described by $N$ copies of a topological Ising CFT. The full interacting model exhibits conformal symmetry in the IR and an emergent pseudo-Goldstone mode that arises from broken reparametrization symmetry. We find that the effective action of the Goldstone mode matches with the 3D AdS gravity action, viewed as a functional of the boundary metric. We compute the spectral density and show that the leading deviation from conformal invariance looks like a $T \bar{T}$ deformation. We comment on the relation between the IR effective action and Liouville CFT.