Quantum correction to chaos in Schwarzian theory

We derive explicit expressions for a specific subclass of Jackiw-Teitelboim (JT) gravity bilocal correlators, corresponding to degenerate Virasoro representations. On the disk, these degenerate correlators are structurally simple, and they allow us to shed light on the 1/C Schwarzian bilocal perturbation series. In particular, we prove that the series is asymptotic for generic weight h ∉ −ℕ/2. Inspired by its minimal string ancestor, we propose an expression for higher genus corrections to the degenerate correlators. We discuss the extension to the $$ \mathcal{N} $$ N = 1 super JT model. On the disk, we similarly derive properties of the 1/C super-Schwarzian perturbation series, which we independently develop as well. As a byproduct, it is shown that JT supergravity saturates the chaos bound λL = 2π/β at first order in 1/C. We develop the fixed-length amplitudes of Liouville supergravity at the level of the disk partition function, the bulk one-point function and the boundary two-point functions. In particular we compute the minimal superstring fixed length boundary two-point functions, which limit to the super JT degenerate correlators. We give some comments on higher topology at the end.

Section: Jhep04(2021)245mentioning

confidence: 99%

“…in terms of the degenerate matter operator O r,s , the Liouville vertex operator e βφ and the bc ghost c. 17 For the particular case of p = 2 and q = 2m − 1, a single-matrix description is possible, and we only have B 1,s for 1 ≤ s ≤ m − 1. The JT limit corresponds to…”

Section: Minimal String: Boundary Tachyon Correlatorsmentioning

confidence: 99%

Degenerate operators in JT and Liouville (super)gravity

Mertens

2021

“…where we have introduced diagrammatic notation to indicate a single -exchange (similar to diagrams in [49]) between two bilocal operators B…”

Section: Jhep08(2020)002mentioning

confidence: 99%

On the Virasoro six-point identity block and chaos

Anous

Haehl

2020

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge c and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block-corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor SL(2, R) (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large c as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.

“…The semiclassical limit and the first quantum correction to two-point and four-point functions were studied in [23]. Schwarzian perturbation theory has also found applications for higher-point functions [24], while higher loop corrections were analyzed in [25].…”

Section: Introductionmentioning

confidence: 99%

On the perturbative expansion of exact bi-local correlators in JT gravity

Papalini

Seminara

2021

We study the perturbative series associated to bi-local correlators in Jackiw-Teitelboim (JT) gravity, for positive weight λ of the matter CFT operators. Starting from the known exact expression, derived by CFT and gauge theoretical methods, we reproduce the Schwarzian semiclassical expansion beyond leading order. The computation is done for arbitrary temperature and finite boundary distances, in the case of disk and trumpet topologies. A formula presenting the perturbative result (for λ ∈ ℕ/2) at any given order in terms of generalized Apostol-Bernoulli polynomials is also obtained. The limit of zero temperature is then considered, obtaining a compact expression that allows to discuss the asymptotic behaviour of the perturbative series. Finally we highlight the possibility to express the exact result as particular combinations of Mordell integrals.