Bulk reconstruction for spinor fields in AdS/CFT

TL;DR

This paper develops a method to reconstruct free spinor fields in Lorentzian AdS space from dual CFT operators, extending the holographic dictionary to include spinor fields and analyzing their transformation properties.

Contribution

It introduces a detailed reconstruction of bulk spinor fields from boundary data, including mode expansion, extrapolate dictionary, and transformation under the modular Hamiltonian.

Findings

Bulk spinor fields can be reconstructed from boundary operators.

The transformation of bulk fermions under the modular Hamiltonian matches expected spinor Lie derivatives.

Calculated bulk-boundary two-point functions from CFT correlators.

Abstract

We develop the representation of free spinor fields in the bulk of Lorentzian anti-de Sitter space in terms of smeared operators in the dual conformal field theory. To do this we expand the bulk field in a complete set of normalizable modes, work out the extrapolate dictionary for spinor fields, and show that the bulk field can be reconstructed from its near-boundary behavior. In some cases chirality and reality conditions can be imposed in the bulk. We study the action of the CFT modular Hamiltonian on bulk fermions to show that they transform with the expected spinor Lie derivative, and we calculate bulk--boundary two-point functions starting from CFT correlators.