1. Holographic complexity is nonlocal
- Author
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Fu, Zicao, Maloney, Alexander, Marolf, Donald, Maxfield, Henry, and Wang, Zhencheng
- Subjects
AdS-CFT Correspondence ,Black Holes ,hep-th ,gr-qc ,Nuclear & Particles Physics ,Mathematical Sciences ,Physical Sciences - Abstract
We study the "complexity equals volume" (CV) and "complexity equals action"(CA) conjectures by examining moments of of time symmetry for $\rm AdS_3$wormholes having $n$ asymptotic regions and arbitrary (orientable) internaltopology. For either prescription, the complexity relative to $n$ copies of the$M=0$ BTZ black hole takes the form $\Delta C = \alpha c \chi $, where $c$ isthe central charge and $\chi$ is the Euler character of the bulk time-symmetricsurface. The coefficients $\alpha_V = -4\pi/3$, $\alpha_A = 1/6 $ defined by CVand CA are independent of both temperature and any moduli controlling thegeometry inside the black hole. Comparing with the known structure of dual CFTstates in the hot wormhole limit, the temperature and moduli independence of$\alpha_V$, $\alpha_A$ implies that any CFT gate set defining either complexitycannot be local. In particular, the complexity of an efficient quantum circuitbuilding local thermofield-double-like entanglement of thermal-sized patchesdoes not depend on the separation of the patches so entangled. We also commenton implications of the (positive) sign found for $\alpha_A$, which requires theassociated complexity to decrease when handles are added to our wormhole.
- Published
- 2018