Quantum chaos and pole skipping in two-dimensional conformal perturbation theory

Abstract

We analyze pole skipping of stress tensor two-point functions in two-dimensional quantum field theories perturbed away from conformality by a relevant deformation. The retarded two-point Green's function can be formally computed in conformal perturbation theory, though it results in singular expressions. We propose a natural interpretation of these expressions and compute the resulting Green's function to leading nontrivial order in the deformation. As a check of our results, we compare the Lyapunov exponents and butterfly velocities we find from our computed skipped poles to those obtained from both a leading-order conformal field theory analysis using Ward identities, as well as to a holographic gravitational dual perturbed by a massive scalar field; we find precise agreement. We comment on extensions to sub-leading order, where agreement with holographic expectations would no longer be expected.

32 pages + 13 pages of appendices, 6 figures. v2: Various minor corrections plus a new section on calculations using the conformal Ward identity and comments on the role of contact terms. v3: fixed some sign errors and checked internal consistency of sign conventions, plus other small edits. Main conclusions remain the same. (version submitted to JHEP)