Bulk reconstruction for spinor fields in AdS/CFT

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.

arXiv comment31 pages

References in corpus (16)

• Gauge Theory Correlators from Non-Critical String Theory
• AdS/CFT Correspondence and Symmetry Breaking
• Relative entropy equals bulk relative entropy
• Spinors and the AdS/CFT correspondence
• Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields
• Constructing local bulk observables in interacting AdS/CFT
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
• Holographic representation of bulk fields with spin in AdS/CFT
• Boundary terms in the AdS/CFT correspondence for spinor fields
• Local bulk physics from intersecting modular Hamiltonians
• Spinor Exchange in AdS_{d+1}
• TASI Lectures on the Emergence of the Bulk in AdS/CFT
• Emergence of spacetime from the algebra of total modular Hamiltonians
• Boundary-to-bulk maps for AdS causal wedges and RG flow

Cited by in corpus (7)

• Symmetry-resolved modular correlation functions in free fermionic theories
• Bulk reconstruction in rotating BTZ black hole
• Lectures on Bulk Reconstruction
• Extension of the HKLL bulk reconstruction for small $\Delta$
• CFT reconstruction of local bulk operators in half-Minkowski space
• Bulk reconstruction and Bogoliubov transformations in AdS${}_2$
• Dressing bulk spinor fields in AdS${}_3$