Causal Evolutions of Bulk Local Excitations from CFT

TL;DR

This paper investigates how localized bulk excitations in AdS spacetime influence boundary two-point functions in 2D CFTs, revealing causal propagation consistent with gravity duals in holographic theories but not in free fermion CFTs.

Contribution

It demonstrates the causal behavior of boundary correlators in holographic CFTs due to bulk excitations and uncovers universal short-distance properties related to entanglement entropy.

Findings

Causal propagation observed in holographic CFTs near the BF bound.

No causal propagation seen in free fermion CFTs.

Universal short-distance behavior of two-point functions related to entanglement entropy.

Abstract

Bulk localized excited states in an AdS spacetime can be constructed from Ishibashi states with respect to the global conformal symmetry in the dual CFT. We study boundary two point functions of primary operators in the presence of bulk localized excitations in two dimensional CFTs. From two point functions in holographic CFTs, we observe causal propagations of radiations when the mass of dual bulk scalar field is close to the BF bound. This behavior for holographic CFTs is consistent with the locality and causality in classical gravity duals. We also show that this cannot be seen in free fermion CFTs. Moreover, we find that the short distance behavior of two point functions is universal and obeys the relation which generalizes the first law of entanglement entropy.