Precursors and BRST Symmetry

TL;DR

This paper explores the encoding of bulk information in the boundary CFT within the AdS/CFT framework, using BRST symmetry to understand precursor ambiguities and their localization in entanglement wedges.

Contribution

It introduces a BRST-based formalism to analyze precursor ambiguities and demonstrates their role in localizing bulk information in the boundary theory.

Findings

Precursor ambiguity can be characterized as BRST exact and ghost-free.

The formalism reproduces known precursor ambiguities in a simple model.

The number of parameters matches the freedom to localize precursors within entanglement wedges.

Abstract

In the AdS/CFT correspondence, bulk information appears to be encoded in the CFT in a redundant way. A local bulk field corresponds to many different non-local CFT operators (precursors). We recast this ambiguity in the language of BRST symmetry, and propose that in the large $N$ limit, the difference between two precursors is a BRST exact and ghost-free term. Using the BRST formalism and working in a simple model with global symmetries, we re-derive a precursor ambiguity appearing in earlier work. Finally, we show within this model that this BRST ambiguity has the right number of parameters to explain the freedom to localize precursors within the boundary of an entanglement wedge order by order in the large $N$ expansion.