Information Scrambling with Higher-Form Fields

TL;DR

This paper investigates the late-time behavior of out-of-time-ordered correlators (OTOCs) involving higher-form conserved currents in holographic theories, revealing universal power-law decay patterns for these correlators.

Contribution

It generalizes the late-time OTOC behavior from $U(1)$ currents to higher-form symmetries and explores their dynamics in various dimensions using holographic duality.

Findings

OTOCs involving higher-form fields exhibit power-law tails at late times.

The study extends the understanding of chaos and information scrambling to generalized symmetries.

Regularization of divergences involves double trace deformations in the boundary theory.

Abstract

The late time behaviour of OTOCs involving generic non-conserved local operators show exponential decay in chaotic many body systems. However, it has been recently observed that for certain holographic theories, the OTOC involving the $U(1)$ conserved current for a gauge field instead varies diffusively at late times. The present work generalizes this observation to conserved currents corresponding to higher-form symmetries that belong to a wider class of symmetries known as generalized symmetries. We started by computing the late time behaviour of OTOCs involving $U(1)$ current operators in five dimensional AdS-Schwarzschild black hole geometry for the 2-form antisymmetric $B$-fields. The bulk solution for the $B$-field exhibits logarithmic divergences near the asymptotic AdS boundary which can be regularized by introducing a double trace deformation in the boundary CFT. Finally, we consider the more general case with antisymmetric $p$-form fields in arbitrary dimensions. In the scattering approach, the boundary OTOC can be written as an inner product between asymptotic 'in' and 'out' states which in our case is equivalent to computing the inner product between two bulk fields with and without a shockwave background. We observe that the late time OTOCs have power law tails which seems to be a universal feature of the higher-form fields with $U(1)$ charge conservation.