Chaos in Celestial CFT

Abstract

Celestial holography proposes a duality between gravitational scattering in asymptotically flat spacetime and a conformal field theory living on the celestial sphere. Its dictionary relates the infinite dimensional space-time symmetry group to Ward identities of the CFT. The spontaneous breaking of these asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here we show that this sector encodes non-trivial backreaction effects that exhibit characteristics of maximal quantum chaos. A key element in the derivation is the identification of the Hilbert space of celestial CFT, defined through radial quantization, with that of a constantly accelerating Rindler observer. From the point of view of the bulk, Rindler particles exhibit Lyapunov behavior due to shockwave interactions that shift the observer horizon. From the point of view of the boundary, the superrotation Goldstone modes affect the relevant representations of the celestial Virasoro symmetry in a manner that induces Lyapunov behavior of out-of-time-ordered celestial correlators.

Mapping SYK to the Sky

“…In combination, these results hint at a structure that ties together the observation of our recent paper [16] on how signals of maximal quantum chaos are encoded in the superrotation Goldstone modes with the presence of celestial w 1+∞ symmetry [18]. Fortuitously, while the perspective in [16] ignored the w 1+∞ structure, it naturally led us to revisit 2D SYK models of the type proposed in [25]. These models precisely have these extra symmetries but hitherto lacked an obvious application or purpose for them.…”

“…Moreover, for the version of the model considered in [25], it was found that the IR Schwinger-Dyson equation exhibits conformal symmetry and that the emergent pseudo-Goldstone action arising from broken reparameterization invariance matches the boundary action derived from 3D AdS gravity. This latter match hints at a potential application to celestial holography, given the analysis in our recent paper [16].…”

“…In the recent paper [16], we applied both of these approaches to the celestial Virasoro symmetry, identifying a sector with large central charge that incorporates backreaction effects and exhibits maximal quantum chaos. By focusing on the connection between radial evolution in the celestial CFT and Rindler evolution in the bulk we were able to observe Lyapunov behavior without needing to add horizons in the bulk -the observer horizon of the Rindler trajectories taking its place.…”

“…We are led to the following question: can we build a model that incorporates the full set of infinite dimensional symmetry enhancements associated to 4D gravity and gives an origin for the signals of chaos we saw in [16]? The goal of this paper is to answer in the affirmative.…”

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

“…In [8], the supersymmetric w 1+∞ algebra has been identified with the corresponding soft current algebra in the supersymmetric Einstein-Yang-Mills theory. The relevant works on the celestial holography in the various directions can be found in [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. See [1] for more complete literatures.…”