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

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.

arXiv comment73 pages, 13 figures; v2: references added

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Cited by in corpus (12)

• Krylov complexity in large-$q$ and double-scaled SYK model
• Correlators of double scaled SYK at one-loop
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• de Sitter versus anti-de Sitter in Horndeski-like gravity
• Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model
• Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• SYK Model with global symmetries in the double scaling limit
• Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry
• Off-diagonal coupling of supersymmetric SYK model
• Schur Connections: Chord Counting, Line Operators, and Indices
• Bosonic near-CFT${}_1$ models from Fock-space fluxes