2018/01/31 by Zicao Fu, Alexander Maloney, Donald Marolf +2 · 5 citations
Mathematics · Physics and Astronomy · #BTZ black hole #Black Holes and Theoretical Physics #Black brane #Black hole (networking) #Central charge #Charge (physics) #Circuit complexity #Combinatorics #Cosmology and Gravitation Theories #Euler characteristic #Extremal black hole #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #Sign (mathematics) #Topology (electrical circuits) #Wormhole #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep02(2018)072
published as JHEP02(2018)072 · 17 pages, 4 figures; v2: minor modifications
arxiv created 2018/01/31 · openalex publication_date 2018/02/01 · arxiv updated 2018/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the “complexity equals volume” (CV) and “complexity equals action” (CA) conjectures by examining moments of of time symmetry for AdS3 wormholes having n asymptotic regions and arbitrary (orientable) internal topology. For either prescription, the complexity relative to n copies of the M = 0 BTZ black hole takes the form ΔC = αcχ, where c is the central charge and χ is the Euler character of the bulk time-symmetric surface. The coefficients α V = −4π/3, α A = 1/6 defined by CV and CA are independent of both temperature and any moduli controlling the geometry inside the black hole. Comparing with the known structure of dual CFT states in the hot wormhole limit, the temperature and moduli independence of α V , α A implies that any CFT gate set defining either complexity cannot be local. In particular, the complexity of an efficient quantum circuit building local thermofield-double-like entanglement of thermal-sized patches does not depend on the separation of the patches so entangled. We also comment on implications of the (positive) sign found for α A , which requires the associated complexity to decrease when handles are added to our wormhole.