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Holographic CCFT Pseudo-Entropy

Reza Fareghbal, Abolfazl Hassani Majoulan

TL;DR

This work analyzes holographic pseudo-entropy for Carrollian CFTs (CCFTs) dual to three-dimensional Minkowski space, showing that both spacelike and timelike extremal curves admit a well-defined flat-space limit. The real part of the pseudo-entropy arises from spacelike curve lengths, while the imaginary part comes from timelike curves, supporting a non-unitary CCFT interpretation. By tracing both AdS/CFT and dS/CFT routes and performing the flat-space limit, the authors establish a consistent holographic picture in which CCFT entanglement is inherently pseudo-entropy. The results reinforce the flat/CCFT dictionary and motivate extensions to higher dimensions and explicit CCFT calculations to confirm the non-unitary nature of CCFTs and the holographic interpretation of 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, and these theories are non-unitary.

Holographic CCFT Pseudo-Entropy

TL;DR

This work analyzes holographic pseudo-entropy for Carrollian CFTs (CCFTs) dual to three-dimensional Minkowski space, showing that both spacelike and timelike extremal curves admit a well-defined flat-space limit. The real part of the pseudo-entropy arises from spacelike curve lengths, while the imaginary part comes from timelike curves, supporting a non-unitary CCFT interpretation. By tracing both AdS/CFT and dS/CFT routes and performing the flat-space limit, the authors establish a consistent holographic picture in which CCFT entanglement is inherently pseudo-entropy. The results reinforce the flat/CCFT dictionary and motivate extensions to higher dimensions and explicit CCFT calculations to confirm the non-unitary nature of CCFTs and the holographic interpretation of 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/CFT, 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, and these theories are non-unitary.

Paper Structure

This paper contains 9 sections, 43 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Entanglement entropy and pseudo-entropy in quantum field theory
  4. The Flat/CCFT correspondence
  5. Flat-space limit of holographic pseudo-entropy in AdS spacetime
  6. Extremal curves and their flat-space limit
  7. Length of timelike and spacelike curves and taking their flat-space limit
  8. Pseudo-entropy in CCFT via dS/CFT correspondence
  9. Summary and future directions

Figures (4)

  • Figure 1: Spacelike (blue) and timelike (red) extremal curves in PoincarĂ© coordinates which are holographic dual of timelike entanglement entropy of timelike interval $A$ (green line) in the boundary CFT.
  • Figure 2: Spacelike and timelike extremal curves in BMS-AdS coordinate which are holographic dual of timelike entanglement entropy. Blue curve is spacelike and red curve is timelike. $A$ (green line) is timelike interval at the boundary.
  • Figure 3: Extremal curves in flat spacetimes written in BMS coordinate. Spacelike curve is blue and timelike curve is red. The length of these curves are proportional to the pseudo-entropy of an interval in CCFT.
  • Figure 4: Spacelike (blue) and timelike (red) extremal curves in dS$_3$ which are holographic dual of pseudo-entropy. $A$ (green) is an arbitrary interval in CFT.