Size of bulk fermions in the SYK model

Abstract

The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS${}_2$ bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk $\text{SL}(2;\mathbb{R})$ generators.

References and minor clarifications added, a typo fix, updated to reflect JHEP version; 41 pages, 10 figures

References in corpus (4)

• Holographic representation of local bulk operators
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Operator Size for Holographic Field Theories

Cited by in corpus (11)

• Complexity growth of operators in the SYK model and in JT gravity
• Krylov complexity in large-$q$ and double-scaled SYK model
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Scrambling Ability of Quantum Neural Networks Architectures
• Seeing behind black hole horizons in SYK
• Holographic boundary states and dimensionally-reduced braneworld spacetimes
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Sectional curvatures distribution of complexity geometry
• Relativistic Dips in Entangling Power of Gravity
• Operator size growth in Lindbladian SYK
• Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model