Dressing bulk spinor fields in AdS${}_3$

TL;DR

This paper advances bulk reconstruction in AdS3 by explicitly constructing Dirac fermion fields coupled to gauge fields from CFT data, confirming consistency across multiple conditions and computing relevant correlators.

Contribution

It provides a detailed method for reconstructing bulk fermionic fields in AdS3 from CFT, including gauge coupling and three-point functions, extending previous scalar field approaches.

Findings

Bulk Dirac fermion reconstructed from CFT in AdS3.

Consistency of equations of motion, modular flow, and charge distribution conditions.

Computed bulk-boundary three-point function at tree level.

Abstract

We continue the program of bulk reconstruction for fermionic fields. We reconstruct, from the CFT, the Dirac fermion field in $AdS_{3}$ coupled to a Chern-Simon gauge field. We show that the three conditions; solving the equation of motion, satisfying expected transformation under modular flow and a simple charge distribution at infinity are all compatible and all produce the same bulk operator. We also compute the bulk-boundary tree level three point function from the CFT construction.