Bulk Reconstruction and Gauge Invariance

TL;DR

This paper examines bulk reconstruction in holography, highlighting the limitations of the large N approximation in capturing gauge invariance and proposing the need for a gauge-invariant approach to better understand spacetime emergence.

Contribution

It critically analyzes the failure of the N=∞ approximation in bulk reconstruction and emphasizes the importance of gauge invariance for accurate holographic models.

Findings

N=∞ approximation neglects gauge invariance

Entanglement wedge reconstruction may be flawed at finite N

Explicit examples show discrepancies in bulk reconstructions

Abstract

In this paper, we discuss the concept of bulk reconstruction, which involves mapping bulk operators into CFT operators to understand the emergence of spacetime and gravity. We argue that the $N=\infty$ approximation fails to capture crucial aspects of gravity, as it does not respect gauge invariance and lacks direct connections between energy and boundary metrics. Key concepts such as entanglement wedge reconstruction and holographic error correction codes, which are based on the $N=\infty$ theory, may be incorrect or require significant revision when finite $N$ effects are considered. We present explicit examples demonstrating discrepancies in bulk reconstructions and suggest that a gauge-invariant approach is necessary for an accurate understanding.