An obstacle to sub-AdS holography for SYK-like models

TL;DR

The paper investigates the limitations of SYK-like models for sub-AdS holography, linking stringy effects to the branching time and establishing bounds that challenge their candidacy for such holographic duals.

Contribution

It introduces a bound on the branching time in SYK-like models and relates it to key dynamical quantities, highlighting obstacles for sub-AdS holography.

Findings

Stringy effects relate to the branching time in SYK models.

A bound on the branching time is derived under ladder diagram assumptions.

The models are unlikely to support sub-AdS holography due to these bounds.

Abstract

We argue that "stringy" effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.