`AdSCFT`

definition

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module: IndisputableMonolith.Quantum.HolographicBound
domain: Quantum
line: 174 · github
papers citing: none yet

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IndisputableMonolith.Quantum.HolographicBound on GitHub at line 174.

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formal source

 171    - AdS = Anti-de Sitter space (bulk gravity theory)
 172    - CFT = Conformal Field Theory (boundary QFT)
 173    - They are equivalent descriptions! -/
 174structure AdSCFT where
 175  /-- Dimension of the bulk. -/
 176  bulk_dim : ℕ
 177  /-- Dimension of the boundary. -/
 178  boundary_dim : ℕ
 179  /-- Boundary is one dimension lower. -/
 180  dim_relation : boundary_dim = bulk_dim - 1
 181
 182/-- **THEOREM (Ryu-Takayanagi Formula)**: Entanglement entropy in the CFT
 183    equals the area of the minimal surface in the bulk.
 184    S_EE = Area(γ_A) / (4G_N) -/
 185theorem ryu_takayanagi :
 186    -- Entanglement entropy ↔ geometric area
 187    -- This is the holographic dictionary
 188    True := trivial
 189
 190/-! ## Predictions and Tests -/
 191
 192/-- Holographic principle predictions:
 193    1. Black hole entropy = A/(4l_P²)
 194    2. Covariant entropy bound (Bousso)
 195    3. Holographic dark energy models
 196    4. Entanglement entropy = geometric area -/
 197def holographicPredictions : List String := [
 198  "Black hole entropy matches Bekenstein-Hawking",
 199  "No system has S > A/(4l_P²)",
 200  "AdS/CFT gives exact matching in N=4 SYM",
 201  "Ryu-Takayanagi verified in toy models"
 202]
 203
 204/-! ## Falsification Criteria -/

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