Statement
Problem 2.8 of Goto et al.: what is the gravity dual of a boundary resource theory — i.e. a resource theory whose free states are holographic states (those with semiclassical duals), whose free operations preserve that class, and whose monotones admit geometric/gravitational descriptions?
Why It Matters
This is the holographic capstone of Theme 1 and the natural home of the group’s most gravitational project: the generalized-entropy-as-capacity result is a concrete fragment of a holographic resource theory — a bulk-geometric monotone (generalized entropy) governing an operational rate (holographic embezzlement).
What We Know
- Free “holographic states” = fixed-area / semiclassical states; entanglement-wedge structure constrains achievable transformations.
- Generalized entropy and entanglement-wedge cross-section already behave as bulk-geometric monotones.
- No complete free-operation/monotone axiomatization exists yet.
Possible Approaches
- Promote the embezzlement-capacity theorem to a monotone statement in a holographic resource theory.
- Identify the bulk operation dual to a boundary free operation (e.g. area-preserving / RT-preserving maps).