Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of conformal field theory to periodically driven systems, the so-called Floquet-driven CFTs. A number of recent works have found that there are classes of periodically driven ( $1+1$ )-dimensional CFTs that can be analytically solved, and that show both heating and nonheating phases, as well as unusual properties in terms of information scrambling. Hitherto, most results have focused on the dynamics of such models at stroboscopic times, i.e., samples taken at each period of the time evolution. In this paper, we consider time evolution at arbitrary real times and derive formulas for the exact time propagation of heating and nonheating classes of Floquet-driven CFTs. This requires a subtle treatment of nonstroboscopic time that leads to different interpretations in terms of curved space-time dynamics in these systems compared to previous results in the literature.Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of conformal field theory to periodically driven systems, the so-called Floquet-driven CFTs. A number of recent works have found that there are classes of periodically driven ($1+1$)-dimensional CFTs that can be analytically solved, and that show both heating and nonheating phases, as well as unusual properties in terms of information scrambling. Hitherto, most results have focused on the dynamics of such models at stroboscopic times, i.e., samples taken at each period of the time evolution. In this paper, we consider time evolution at arbitrary real times and derive formulas for the exact time propagation of heating and nonheating classes of Floquet-driven CFTs. This requires a subtle treatment of nonstroboscopic time that leads to different interpretations in terms of curved space-time dynamics in these systems compared to previous results in the literature.

arXiv:2011.08494Physical review. D/Physical review. D.Mar 10, 202117 citations

Quantum chaos in Liouville CFT

Julian Sonner, Benjamin Strittmatter

A bstract Fast scrambling is a distinctive feature of quantum gravity, which by means of holography is closely tied to the behaviour of large- c conformal field theories. We study this phenomenon in the context of semiclassical Liouville theory, providing both insights into the mechanism of scrambling in CFTs and into the structure of Liouville theory, finding that it exhibits a maximal Lyapunov exponent despite not featuring the identity in its spectrum. However, as we show, the states contributing to the relevant correlation function can be thought of as dressed scramblons. At a technical level we first use the path integral picture in order to derive the Euclidean four-point function in an explicit compact form. Next, we demonstrate its equivalence to a conformal block expansion, revealing an explicit but non-local map between path integral saddles and conformal blocks. By analytically continuing both expressions to Lorentzian times, we obtain two equivalent formulations of the OTOC, which we use to study the onset of chaos in Liouville theory. We take advantage of the compact form in order to extract a Lyapunov exponent and a scrambling time. From the conformal block expansion formulation of the OTOC we learn that scrambling shifts the dominance of conformal blocks from heavy primaries at early times to the lightest primary at late times. Finally, we discuss our results in the context of holography.A bstract Fast scrambling is a distinctive feature of quantum gravity, which by means of holography is closely tied to the behaviour of large- c conformal field theories. We study this phenomenon in the context of semiclassical Liouville theory, providing both insights into the mechanism of scrambling in CFTs and into the structure of Liouville theory, finding that it exhibits a maximal Lyapunov exponent despite not featuring the identity in its spectrum. However, as we show, the states contributing to the relevant correlation function can be thought of as dressed scramblons. At a technical level we first use the path integral picture in order to derive the Euclidean four-point function in an explicit compact form. Next, we demonstrate its equivalence to a conformal block expansion, revealing an explicit but non-local map between path integral saddles and conformal blocks. By analytically continuing both expressions to Lorentzian times, we obtain two equivalent formulations of the OTOC, which we use to study the onset of chaos in Liouville theory. We take advantage of the compact form in order to extract a Lyapunov exponent and a scrambling time. From the conformal block expansion formulation of the OTOC we learn that scrambling shifts the dominance of conformal blocks from heavy primaries at early times to the lightest primary at late times. Finally, we discuss our results in the context of holography.

arXiv:2407.11124Journal of High Energy PhysicsMay 2, 20251 citation

Scrambling in two-dimensional conformal field theories with light and smeared operators

Harsha R. Hampapura, Andrew Rolph, Bogdan Stoica

We study quantum chaos in two-dimensional conformal field theories, building on the work analyzing the out-of-time order thermal correlation functions using large- $c$ Virasoro blocks. Our work investigates the contribution of light intermediate channels and smearing length scales to the four-point function and scrambling. Precise relations for how light intermediate channels increase the scrambling time and how smearing length scales smaller than the thermal length scale decrease the scrambling time are derived.We study quantum chaos in two-dimensional conformal field theories, building on the work analyzing the out-of-time order thermal correlation functions using large-$c$ Virasoro blocks. Our work investigates the contribution of light intermediate channels and smearing length scales to the four-point function and scrambling. Precise relations for how light intermediate channels increase the scrambling time and how smearing length scales smaller than the thermal length scale decrease the scrambling time are derived.

arXiv:1809.09651Physical review. D/Physical review. D.May 20, 20199 citations

Sewing conformal field theories I

Hidenori Sonoda

Nuclear Physics BDec 1, 198878 citations

1+1

)-dimensional CFTs that can be analytically solved, and that show both heating and nonheating phases, as well as unusual properties in terms of information scrambling. Hitherto, most results have focused on the dynamics of such models at stroboscopic times, i.e., samples taken at each period of the time evolution. In this paper, we consider time evolution at arbitrary real times and derive formulas for the exact time propagation of heating and nonheating classes of Floquet-driven CFTs. This requires a subtle treatment of nonstroboscopic time that leads to different interpretations in terms of curved space-time dynamics in these systems compared to previous results in the literature.

We study quantum chaos in two-dimensional conformal field theories, building on the work analyzing the out-of-time order thermal correlation functions using large-

c

Virasoro blocks. Our work investigates the contribution of light intermediate channels and smearing length scales to the four-point function and scrambling. Precise relations for how light intermediate channels increase the scrambling time and how smearing length scales smaller than the thermal length scale decrease the scrambling time are derived.