## Classification of out-of-time-order correlators

Felix M. Haehl, R. Loganayagam, Prithvi Narayan, Mukund Rangamani

SciPost Phys. 6, 001 (2019) · published 7 January 2019

- doi: 10.21468/SciPostPhys.6.1.001
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### 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.

### Cited by 3

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^{1 }Felix Haehl, -
^{2 }R. Loganayagam, -
^{2 }Prithvi Narayan, -
^{3 }Mukund Rangamani

^{1}University of British Columbia [UBC]^{2}International Centre for Theoretical Sciences [ICTS-TIFR]^{3}University of California, Davis [UCD]