Complex Sachdev-Ye-Kitaev model in the double scaling limit

TL;DR

This paper provides an exact solution for the energy spectrum and correlation functions of the complex SYK model in the double scaling limit, revealing detailed insights into its spectral and gravitational properties across all energy scales.

Contribution

It introduces a comprehensive analysis of the complex SYK model with a $U(1)$ symmetry, including fixed charge sectors, spectral asymmetry, and effects of heavy operators, extending the chord diagram framework.

Findings

Exact energy spectrum and correlation functions at all energy scales.

Incorporation of chemical potential and fixed charge sectors.

Exact computation of heavy operator effects and spacetime interfaces.

Abstract

We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a $U(1)$ global symmetry. The analysis shows how to incorporate a chemical potential in the chord diagram picture, and we present results for the various observables also at a given fixed charge sector. In addition to matching to the spectral asymmetry, we consider an analogous asymmetry measure of the 2-point function obeying a non-trivial dependence on the operator's dimension. We also provide the chord diagram structure for an SYK-like model that has a $U(M)$ global symmetry at any disorder realization. We then show how to exactly compute the effect of inserting very heavy operators, with formally infinite conformal dimension. The latter separate the gravitational spacetime into several parts connected by an interface, whose properties are exactly computable at all scales. In particular, light enough states can still go between the spaces. This behavior has a simple description in the chord diagram picture.