Chaos and the reparametrization mode on the AdS2 string

Abstract

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 $$ \mathcal{N} $$ 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.

Bootstrapping perturbative and non-perturbative defect correlators

“…In this limit, all the perturbative orders of the leading behaviour can be fixed and resummed using the Borel transform. This matches computations done independently in [28] and constitutes some non-perturbative aspects of the correlator. Let us define the function related to (1) by…”

“…. This matches equation (3.20) in [28] if we identify ∆ V = ∆ W = 1 2 , corresponding to the conformal weight of the superconformal primary. This formalism in terms of conformal blocs is a reorganising of the perturbative series, where the (partially unmixed) conformal data is in reality contained in all perturbative orders as the leading powers of logarithms.…”

“…The 4-point case was bootstrapped in [19]. However, the analytic bootstrap technique is not restricted to this case and can be applied for higher-point functions of recent interest [18,20,21]. In this context, we study the correlator…”

“…From this a number of conclusions can be drawn; the first as that the mixing of operators does not happenat this order, the second is the CFT data presented in [11,26,27]. One can also do this for the case for 6-point functions, which is being explored using many different methods such as the numerical bootstrap and explicit computations in the conformal gauge [20,21].…”

“…One of the aspects of the perturbative expansion of the OPE is that the highest power of logarithms at each order is entirely fixed in terms of tree-level CFT data. There is a limit in which this is the leading contribution of the correlator; the double-scaling limit [28]. In this limit, all the perturbative orders of the leading behaviour can be fixed and resummed using the Borel transform.…”