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Effective field theory for chaotic CFTs

Haehl, Felix M., Rozali, Moshe·2018·Journal of High Energy Physics
DOI 10.1007/jhep10(2018)118
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Abstract

We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss the gauge symmetries of the model and how they relate to the Lyapunov behaviour of certain correlators. We calculate the out-of-time-ordered correlators diagnosing quantum chaos, as well as certain more fine-grained higher-point generalizations, using our Lorentzian effective field theory. We comment on potential future applications of the effective theory to real-time thermal physics and conformal field theory.

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Figures

Figure 1 Contours in the complex ω -plane, defining the retarded, advanced, and Keldysh (symmetric) correlation functions, respectively. The contour C K = C R -C A . The red crosses denote the poles of the integrand at ω ∈ {-i, 0 ± iε, i } , where ε > 0 is a small regulator that enforces consistent boundary conditions.
Figure 1 Contours in the complex ω -plane, defining the retarded, advanced, and Keldysh (symmetric) correlation functions, respectively. The contour C K = C R -C A . The red crosses denote the poles of the integrand at ω ∈ {-i, 0 ± iε, i } , where ε > 0 is a small regulator that enforces consistent boundary conditions.CC-BY · From the PDF
Figure 2 We choose the k -OTO contour in the complex time plane to be such that all legs are equally separated by ϕ in the imaginary direction. We often set either ϕ = π k (equal separations) or ϕ = δ ≪ 1 (small separation limit). The legs of the contour are labelled by indices α, β, . . . = 1 , . . . , 2 k .
Figure 2 We choose the k -OTO contour in the complex time plane to be such that all legs are equally separated by ϕ in the imaginary direction. We often set either ϕ = π k (equal separations) or ϕ = δ ≪ 1 (small separation limit). The legs of the contour are labelled by indices α, β, . . . = 1 , . . . , 2 k .CC-BY · From the PDF
Figure 3 Illustration of the 4- and 6-point out-of-time-ordered correlators that we consider.
Figure 3 Illustration of the 4- and 6-point out-of-time-ordered correlators that we consider.CC-BY · From the PDF
Figure 4 Illustration of the arrangement of operators in our 2 k -point observable F 2 k , for the case k = 5. It provides a generalization of the familiar 4-point OTOC, which has the property that the associated time of exponential growth (which we call as k -scrambling time t ( k ) ∗ ) is maximal: t ( k ) ∗ = ( k -1) log c . The red solid lines indicate bilocal operators B ( h, ¯ h ) . The red wiggly lines schematically indicate the (maximally braided) propagation of the scrambling mode ϵ .
Figure 4 Illustration of the arrangement of operators in our 2 k -point observable F 2 k , for the case k = 5. It provides a generalization of the familiar 4-point OTOC, which has the property that the associated time of exponential growth (which we call as k -scrambling time t ( k ) ∗ ) is maximal: t ( k ) ∗ = ( k -1) log c . The red solid lines indicate bilocal operators B ( h, ¯ h ) . The red wiggly lines schematically indicate the (maximally braided) propagation of the scrambling mode ϵ .CC-BY · From the PDF

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Metadata

Authors
Haehl, F. M., & Rozali, M.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2018-10
Volume
2018
Issue
10
ISSN
1029-8479
DOI
10.1007/jhep10(2018)118
Cited by
96
References
3
Language
en
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CoChat. (2026). Citation check: Effective field theory for chaotic CFTs. https://app.cochat.ai/papers/10.1007/jhep10(2018)118
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Haehl, F. M., & Rozali, M. (2018). Effective field theory for chaotic CFTs. Journal of High Energy Physics. https://doi.org/10.1007/jhep10(2018)118