Holographic Dictionary

Definition

The holographic dictionary is the operational map between a $d$-dimensional CFT (the “boundary”) and a $(d+1)$-dimensional gravity theory on asymptotically AdS spacetime (the “bulk”) asserted by gravity duality. It pairs every CFT operator $\mathcal{O}$ of dimension $\Delta$ with a bulk field $\varphi$ of mass $m^2{L}^2=\Delta (\Delta -d)$, identifies boundary sources with bulk boundary conditions via the gkp-witten-formula, and maps CFT correlators to bulk on-shell actions.

Role in Research

The dictionary is the central organizing apparatus of Lectures 12–16 of the holography course. In the wiki, it is the bridge from the algebraic-QFT-side type III₁ structure (active research) to the bulk geometric picture of black-hole entropy.

Relations

• gkp-witten-formula — the formal statement equating CFT generating functional with bulk on-shell action.
• large-n-factorization — the boundary-side fact that makes the bulk-side classical-gravity limit possible.
• ryu-takayanagi-formula — the entropy entry in the dictionary.
• subregion-subalgebra-duality — the algebraic refinement of bulk reconstruction.

Papers

• Aharony–Gubser–Maldacena–Ooguri–Oz, Large N field theories, string theory and gravity, Phys. Rep. 323 (2000) 183, arXiv:hep-th/9905111.
• McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518.

Notes

Course coverage: Lecture 13 and Lecture 15; bulk reconstruction in Lecture 18.