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Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
Daniel A Roberts1, Douglas Stanford2
1Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|October 10, 2015
Summary
We investigate chaotic dynamics in 2D conformal field theory using out-of-time-order correlators. Our findings reveal exponential decay in thermal correlators, providing insights into quantum chaos and scrambling times.
Area of Science:
- Quantum Field Theory
- Statistical Mechanics
- High Energy Physics
Background:
- Chaotic dynamics are crucial for understanding thermalization in quantum systems.
- Conformal Field Theories (CFTs) provide a powerful framework for studying critical phenomena.
- Out-of-time-order correlators (OTOCs) are key probes of quantum chaos.
Purpose of the Study:
- To study chaotic dynamics in two-dimensional conformal field theories (2D CFTs).
- To analyze the behavior of thermal correlators of the form ⟨W(t)VW(t)V⟩.
- To connect holographic calculations with CFT methods for understanding quantum chaos.
Main Methods:
- Utilizing out-of-time-order thermal correlators.
- Studying the large c Virasoro identity conformal block.
- Reproducing holographic calculations inspired by Shenker and Stanford.
Main Results:
- The conformal block contribution to the correlation function exhibits exponential decay.
- This decay begins after a characteristic scrambling time, t*.
- The scrambling time is related to the central charge (c) and operator energy scales (Ew, Ev).
Conclusions:
- The study provides a CFT perspective on holographic calculations of quantum chaos.
- It elucidates the role of conformal blocks in thermal correlator dynamics.
- The results offer insights into the nature of fast scrambling in quantum systems.
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