Holographic CCFT Pseudo-Entropy

TL;DR

This paper explores the holographic pseudo-entropy in Carrollian conformal field theories (CCFT) and demonstrates that entanglement entropy in CCFTs is fundamentally a form of pseudo-entropy, extending holographic principles to flat spacetimes.

Contribution

It establishes a holographic interpretation of pseudo-entropy in CCFTs and connects extremal curves in flat space to the real and imaginary parts of pseudo-entropy.

Findings

Extremal spacelike and timelike curves have a well-defined flat-space limit.

Curve lengths correspond to real and imaginary parts of pseudo-entropy.

Entanglement entropy in CCFTs is fundamentally pseudo-entropy.

Abstract

According to the flat/CCFT correspondence, Carrollian conformal field theories (CCFT) in d dimensions are dual to asymptotically flat spacetimes in d+1 dimensions. In this paper, starting from the holographic interpretation of pseudo-entropy in the (A)dS$_3$/CFT$_2$, we show that both extremal spacelike and timelike curves possess a well-defined flat-space limit. The length of these curves can be regarded as the real and imaginary parts of the pseudo-entropy for the underlying field theory, where only the real part has been considered thus far. Our calculations can confirm that the entanglement entropy in the CCFTs is fundamentally pseudo-entropy.