Permutation Orbifolds and Chaos

TL;DR

The paper tests chaos in permutation orbifolds by computing out-of-time-ordered correlators at large central charge. It demonstrates that OTOCs do not decay at late times for arbitrary low-dimension operators, indicating non-chaotic behavior consistent with the theories being free discrete gauge theories with large-N factorization. This non-chaotic result holds for both untwisted and twisted sectors and is governed by seed-theory OTO data through a controlled 1/N expansion. The work also discusses early-time dependence on the seed theory and comments on possible maximal chaos under deformation to strong coupling, highlighting the role of orbifold structure in suppressing chaotic dynamics.

Abstract

We study out-of-time-ordered correlation functions in permutation orbifolds at large central charge. We show that they do not decay at late times for arbitrary choices of low-dimension operators, indicating that permutation orbifolds are non-chaotic theories. This is in agreement with the fact they are free discrete gauge theories and should be integrable rather than chaotic. We comment on the early-time behaviour of the correlators as well as the deformation to strong coupling.