Permutation Orbifolds and Chaos

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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.

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Two-dimensional conformal field theory and the butterfly effect

, (2015)

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time order thermal correlators of the form \(\langle W(t)VW(t)V\rangle\). We reproduce bulk calculations similar to those of [1], by studying the large \(c\) Virasoro identity block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of \(\sim t_* - \frac{\beta}{2\pi}\log \beta^2E_w E_v\), where \(t_*\) is the scrambling time \(\frac{\beta}{2\pi}\log c\), and \(E_w,E_v\) are the energy scales of the \(W,V\) operators.

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Correlation functions for M^N/S_N orbifolds

Samir D. Mathur, Oleg Lunin (2000)

We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is `universal' in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion principle.