In this talk we will present the computation of OTOCs in two-dimensional holographic CFTs with different left- and right-moving temperatures. Depending on whether the CFT lives on a spatial line or circle, the dual bulk geometry is a boosted BTZ black brane or a rotating BTZ black hole. In the case when the spatial direction is non-compact, we generalise a computation of Roberts and Stanford and show that to reproduce the correct bulk answer a maximal channel contribution needs to be selected when using the identity block approximation. We use the correspondence between global conformal blocks and geodesic Witten diagrams to extend our results to CFTs on a spatial circle.
Furthermore, we will consider the OTOC in a zero temperature 2d CFT under evolution by a Liouvillian composed of the Virasoro generators other than L_0. A bound was conjectured on the growth of the OTOC set by the Krylov complexity which is a measure of operator growth. The latter grows as an exponential in time with an exponent which sets an upper bound on the Lyapunov exponent. We show that these Virasoro generators form the modular Hamiltonian of the CFT with half space traced out, thus giving rise to thermal dynamics in a zero temperature CFT. Leveraging the thermal dynamics of the system, we derive this bound in a zero temperature CFT using the analyticity and boundedness properties of the OTOC.
Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911