# Operator growth in 2d CFT

@article{Caputa2021OperatorGI, title={Operator growth in 2d CFT}, author={Pawel Caputa and Shouvik Datta}, journal={Journal of High Energy Physics}, year={2021} }

Abstract
We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos algorithm and evaluate the Krylov complexity of simple operators (primaries and the stress tensor) under a unitary evolution protocol. Evolution of primary operators proceeds as a flow into the ‘bath of descendants’ of the Verma module. These…

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## References

SHOWING 1-10 OF 60 REFERENCES

Symmetries near the horizon

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We consider a nearly-AdS2 gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS2 which move bulk matter relative to the dynamical…

Quantum thermalization and Virasoro symmetry

- Physics
- 2019

We initiate a systematic study of high energy matrix elements of local operators in 2d CFT. Knowledge of these is required in order to determine whether the eigenstate thermalization hypothesis (ETH)…

Unveiling Operator Growth Using Spin Correlation Functions

- Medicine, Computer ScienceEntropy
- 2021

It is argued that it is possible to distinguish between operator-hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems.

Typicality and thermality in 2d CFT

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We identify typical high energy eigenstates in two-dimensional conformal field theories at finite c and establish that correlation functions of the stress tensor in such states are…

Exact Correlators of Giant Gravitons from dual N=4 SYM

- Mathematics, Physics
- 2001

A class of correlation functions of half-BPS composite operators are computed exactly (at finite $N$) in the zero coupling limit of N=4 SYM theory. These have a simple dependence on the…

Operator growth in the SYK model

- PhysicsJournal of High Energy Physics
- 2018

A bstractWe discuss the probability distribution for the “size” of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards…

Generalized Eigenstate Thermalization Hypothesis in 2D Conformal Field Theories.

- Medicine, PhysicsPhysical review letters
- 2019

It is proposed that in the thermodynamic limit large central charge 2D CFTs satisfy generalized eigenstate thermalization, with the values of qKdV charges forming a complete set of thermodynamically relevant quantities, which unambiguously determine expectation values of all local observables from the vacuum family.

Semi-classical Virasoro blocks: proof of exponentiation

- Physics
- 2019

Virasoro conformal blocks are expected to exponentiate in the limit of large central charge c and large operator dimensions h i , with the ratios h i /c held fixed. We prove this by employing the…

A Universal Operator Growth Hypothesis

- PhysicsPhysical Review X
- 2019

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued…

Bounding the space of holographic CFTs with chaos

- Physics
- 2016

A bstractThermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λL ≤ 2π/β. We harness this…