Title: Classification of out-of-time-order correlators,
Abstract: The space of n-point correlation functions, for all possible time-orderings
of operators, can be computed by a non-trivial path integral contour, which
depends on how many time-ordering violations are present in the correlator.
These contours, which have come to be known as timefolds, or out-of-time-order
(OTO) contours, are a natural generalization of the Schwinger-Keldysh contour
(which computes singly out-of-time-ordered correlation functions). We provide a
detailed discussion of such higher OTO functional integrals, explaining their
general structure, and the myriad ways in which a particular correlation
function may be encoded in such contours. Our discussion may be seen as a
natural generalization of the Schwinger-Keldysh formalism to higher OTO
correlation functions. We provide explicit illustration for low point
correlators (n=2,3,4) to exemplify the general statements.