Bulk Point
Kernel
HKLL (2006):
φ(x,z) = ∫ K(x,z;y) O(y) dy
K = smearing kernel, reconstructs local bulk field from boundary operator O.
Smearing kernel:
K(r,θ;φ) ∝ (r cos(θ−φ) − r² cos...)^{Δ−d}
Supported on boundary, peaked near bulk point's causal wedge.
Mass-dimension:
m²L² = Δ(Δ−d)
Lighter fields → smaller Δ → longer reach into bulk.
Breakdown:
Works perturbatively. Non-perturbative: use wedge reconstruction / Python's lunch.
φ(x,z) = ∫ K(x,z;y) O(y) dy
K = smearing kernel, reconstructs local bulk field from boundary operator O.
Smearing kernel:
K(r,θ;φ) ∝ (r cos(θ−φ) − r² cos...)^{Δ−d}
Supported on boundary, peaked near bulk point's causal wedge.
Mass-dimension:
m²L² = Δ(Δ−d)
Lighter fields → smaller Δ → longer reach into bulk.
Breakdown:
Works perturbatively. Non-perturbative: use wedge reconstruction / Python's lunch.