Non-Lorentzian Chaos and Cosmological Holography

Abstract

We study chaos in non-Lorentzian field theories, specifically Galilean and Carrollian conformal field theories in two dimensions. In a large central charge limit, we find that the Lyapunov exponent saturates the bound on chaos, conjectured originally for relativistic field theories. We recover the same Lyapunov exponent holographically by a shock-wave calculation in three-dimensional flat space cosmologies, providing further evidence for flat space holography.

Figures (1)

• Figure 1: Penrose diagram depicting the shock wave FSC geometry. Here the lower (upper) part of the diagram corresponds to a contracting (expanding) universe. The probe is sent out from $\mathscr{I}^-$ and after a reflection at the singularity (wiggly line) emerges from the cosmological horizon (dashed line) where it intersects with the signal very close to the horizon at point $A$ and with the surface $\tau=\tau_c$ at point $B$. Without taking backreactions into account the signal intersects the surface $\tau=\tau_c$ at the point $C$. Taking backreactions into account the observer $O'$ gets shifted to the point $D$ in order to still be able to receive the signal at $\tau=\tau_c$.