2020/12/09 by Pawel Caputa, Jorrit Kruthoff, Onkar Parrikar
Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Conformal field theory #Conformal map #Euclidean geometry #Noncommutative and Quantum Gravity Theories #Path integral formulation #Quantum entanglement #Quantum many-body systems #Superposition principle #Tensor (intrinsic definition) #Wave function #hep-th
paper · pdf · doi:10.1007/jhep05(2021)009
38 pages, 6 figures
arxiv created 2020/12/09 · openalex created_date 2020/12/21 · openalex publication_date 2021/05/03 · arxiv updated 2021/05/19 · openalex updated_date 2026/08/05
A bstract We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral of an effective theory on a family of hyperbolic slices in the dual bulk geometry. The effective theory in question is the CFT flowed under a TT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation, which “folds” the boundary CFT towards the bulk time-reflection symmetric slice. We propose that these novel Euclidean path integral states in the CFT can be interpreted as continuous tensor network (CTN) states. We argue that these CTN states satisfy a Ryu-Takayanagi-like minimal area upper bound on the entanglement entropies of boundary intervals, with the coefficient being equal to \frac14GN <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mrow> <mml:mn>4</mml:mn> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:mrow> </mml:mfrac> </mml:math> ; the CTN corresponding to the bulk time-reflection symmetric slice saturates this bound. We also argue that the original state of the CFT can be written as a superposition of such CTN states, with the corresponding wavefunction being the bulk Hartle-Hawking wavefunction.