[Paper Review] A freely falling graviton in the D1D5 CFT

Bin Guo, Shaun Hampton|arXiv (Cornell University)|Jul 25, 2021

Black Holes and Theoretical Physics4 citations

TL;DR

This paper studies the dynamics of a freely falling graviton in AdS via the D1D5 conformal field theory (CFT), introducing a marginal deformation to model particle splitting. Using numerical computation of scattering amplitudes, it finds early-time linear growth in the splitting amplitude—indicating effective local operator behavior and operator size growth—followed by late-time periodicity, consistent with non-thermalization of a freely falling graviton.

ABSTRACT

We study a freely falling graviton propagating in AdS in the context of the D1D5 CFT, where we introduce an interaction by turning on a deformation operator. We start with one left and right moving boson in the CFT. After applying two deformation operators, the initial bosons split into three left moving and three right moving bosons. We compute the amplitude for various energies and extrapolate the result to the large energy region. At early times, the amplitude is linear in time. This corresponds to an infalling graviton becoming redshifted in AdS. At late times, the amplitude is periodic, which agrees with the fact that a freely falling graviton will not be thermalized.

Motivation & Objective

• To understand the behavior of a freely falling graviton in AdS using the D1D5 CFT with a marginal deformation.
• To investigate how high-energy particles split into lower-energy modes in the strongly coupled CFT.
• To determine whether the splitting process leads to thermalization or remains coherent over time.
• To identify the emergence of an effective local operator at early times and its role in operator size growth.

Proposed method

• Use of a marginal deformation operator in the D1D5 CFT to introduce interactions that enable particle splitting.
• Numerical computation of the splitting amplitude for various initial energies, extrapolating to large energy limits.
• Mapping to a covering space to resolve twist operators arising from the deformation, enabling exact computation of correlation functions.
• Analysis of the time evolution of the amplitude to identify early-time linear growth and late-time periodicity.
• Use of dimensional analysis and effective field theory intuition to interpret the early-time behavior as arising from an effective local operator.
• Comparison with known results in SYK and higher-dimensional toy models to contextualize operator growth behavior.

Experimental results

Research questions

• RQ1 Does the splitting of a high-energy graviton into lower-energy modes in the D1D5 CFT lead to thermalization or remain coherent?
• RQ2 How does the time evolution of the splitting amplitude behave at early and late times?
• RQ3 Can an effective local operator emerge from the interaction of two deformation operators, and what is its role in operator size growth?
• RQ4 What is the nature of the late-time behavior of the amplitude, and how does it relate to the non-thermalization of a freely falling graviton?
• RQ5 How does the splitting process in the deformed D1D5 CFT compare to operator growth in other models like SYK?

Key findings

• At early times (t ≲ π), the splitting amplitude grows linearly with time, indicating effective local operator behavior and consistent with operator size growth.
• At late times (t ≳ π), the amplitude becomes periodic with period 2π, signaling non-thermalization and coherence of the infalling graviton.
• The splitting process is driven by two deformation operators binding together to form an effective local operator, enabling dimensional analysis-based time scaling.
• Numerical results for initial energies m = 18, 24, 30, 36 show that the amplitude coefficients B^{11→11}_{k,k} decrease with increasing k and m, with values ranging from ~10^{-6} to ~10^{-5} for k ≤ 63.
• The absence of secular growth (e.g., t^2 terms) in the amplitude confirms that the system does not thermalize, consistent with the gravity dual of a freely falling graviton.
• The late-time periodicity and lack of thermalization are consistent with the expectation that a freely falling graviton in AdS does not decay into lower-energy states or excite stringy modes.