TY - JOUR
T1 - Chaos and the reparametrization mode on the AdS2 string
AU - Giombi, Simone
AU - Komatsu, Shota
AU - Offertaler, Bendeguz
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/9
Y1 - 2023/9
N2 - We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS2 geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS2 black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS2 string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to SL(2, ℝ) invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in N = 4 SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.
AB - We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS2 geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS2 black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS2 string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to SL(2, ℝ) invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in N = 4 SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.
KW - AdS-CFT Correspondence
KW - Wilson, ’t Hooft and Polyakov loops
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U2 - 10.1007/JHEP09(2023)023
DO - 10.1007/JHEP09(2023)023
M3 - Article
AN - SCOPUS:85169885387
SN - 1126-6708
VL - 2023
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 9
M1 - 23
ER -