2019/08/31 by Yoshiki Sato, Kento Watanabe
Mathematics · Physics and Astronomy · #Action (physics) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary (topology) #Computation #Conformal field theory #Conformal map #Conjecture #Field (mathematics) #Holography #Quantum field theory #Quantum many-body systems #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep11(2019)132
20 pages, 3 figures, v2: section 3.3 & discussion improved
arxiv created 2019/09/19 · openalex publication_date 2019/11/01 · openalex created_date 2019/12/05 · arxiv updated 2020/01/08 · openalex updated_date 2026/08/05
A bstract Recently, Chapman et al. argued that holographic complexities for defects distinguish action from volume. Motivated by their work, we study complexity of quantum states in conformal field theory with boundary. In generic two-dimensional BCFT, we work on the path-integral optimization which gives one of field-theoretic definitions for the complexity. We also perform holographic computations of the complexity in Takayanagi’s AdS/BCFT model following by the “complexity = volume” conjecture and “complexity = action” conjecture. We find that increments of the complexity due to the boundary show the same divergent structures in these models except for the CA complexity in the AdS3/BCFT 2 model as the argument by Chapman et al. . Thus, we conclude that boundary does not distinguish the complexities in general.