Renormalisation Group Flows of Deformed SYK Models

TL;DR

This paper investigates deformations of the SYK model by combining two Hamiltonians with different fermion interactions, analyzing their thermodynamics, RG flows, and holographic duals using analytic and numerical methods.

Contribution

It introduces a new class of deformed SYK models with solvable limits and explores their thermodynamics, RG flows, and holographic interpretations.

Findings

Identification of a novel solvable model in the large q limit

Observation of two linear-in-temperature entropy regions in RG flow

Construction of holographic flow geometries between near-AdS2 spacetimes

Abstract

We explore computationally tractable deformations of the SYK model. The deformed theories are described by the sum of two SYK Hamiltonians with differing numbers, $q$ and $\tilde{q}$, of interacting fermions. In the large $N$ limit, employing analytic and numerical tools, we compute finite temperature correlation functions and thermodynamic quantities. We identify a novel analytically solvable model in the large $q$ limit. We find that, under certain circumstances, the thermal RG flow in the strongly coupled infrared phase exhibits two regions of linear-in-temperature entropy, which we interpret in terms of Schwarzian actions. Using conformal perturbation theory we compute the leading relevant correction away from the intermediate near-conformal fixed point. Holographic spacetimes in two spacetime dimensions that reproduce the thermodynamics of the microphysical theory are discussed. These are flow geometries that interpolate between two Euclidean near-AdS$_2$ spacetimes with different radii. The Schwarzian soft mode corresponding to the AdS$_2$ region in the deep interior resides entirely within the geometric regime.