タイトル：
Flow equation, conformal symmetry, AdS geometries with general conformally
flat boundary
アブストラクト：
In this talk I will speak about my recent works with S.Aoki on the study of
mechanism of emergence of AdS geometry from CFT via flow equation.
A flow equation is a kind of operator renormalization which resolves UV
singularity.
While this was used to help numerical simulation in lattice QCD, there has
recently been a proposal to construct a one higher dimensional geometry
associated with the flow equation in a QFT.
In our recent papers, I investigated aspects of an induced metric with the
collaborator and our main results are the following.
i) Generally an induced metric becomes a quantum information metric called
the Bures or Helstrom metric.
ii) For any CFT, induced metrics explicitly computed match (Poincare) AdS.
iii) Conformal symmetry of CFT converts to the AdS isometry after quantum
averaging. This guarantees the emergence of AdS without explicit
calculation.
iv) We generalize ii) and iii) in the case of any CFT defined on a general
conformally flat manifold.