Holographic Complexity — CV Conjecture

Complexity = Volume of the maximal slice through the wormhole (Wheeler-DeWitt patch)
1.00
1.00
1.50
1.50
C = V/(GL) = 0.00 | dC/dt = 0.00

The Complexity=Volume (CV) conjecture (Susskind 2014) proposes that quantum circuit complexity of the boundary CFT state equals the volume of the maximal Cauchy slice through the AdS-Schwarzschild black hole: C = V_max / GL. At late times, the Wheeler-DeWitt patch grows linearly: dC/dt = 2M (in natural units) — the Lloyd bound. This matches the "complexity never decreases" intuition. The wormhole interior grows indefinitely even after the exterior has thermalized, requiring complexity (not entropy) as the dual observable.