Holographic complexity of cold hyperbolic black holes

The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual of the complexity, including the "Complexity = Volume" (CV) and "Complexity = Action" (CA) prescriptions, and in the harmonic chain with Dirichlet boundary conditions. In all the cases considered except for CA, the boundary introduces a subleading logarithmic divergence in the expansion of the complexity as the UV cutoff vanishes. Holographic subregion complexity is also explored in the CV case, finding that it can change discontinuously under continuous variations of the configuration of the subregion.

Section: Discussionmentioning

confidence: 99%

Complexity in the presence of a boundary

Paolo

Cotrone

Tonni

2020

“…Secondly, in the tensor network description there is a subtle issue that the MERA network can also be interpreted as a de Sitter space [6,11], while the refined tensor networks given in [10,13] are argued to describe Euclidean 2 The relevance of computational complexity in holography was recently pointed out and holographic complexity was conjectured to be the volume of maximal time slice in gravity duals [25,26] (for recent progresses see e.g. [27][28][29][30][31]) and the gravity action in Wheeler-De Witt patch in [32,33] (for recent progresses see e.g. [34][35][36][37][38][39][40][41][42]).…”

Section: Jhep11(2017)097mentioning

confidence: 99%

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Caputa

Kundu

Miyaji

et al. 2017

281

402

Abstract:We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

“…1 Still, some qualitative differences in the AC/VC dichotomy persist, particularly for cold systems, such as near-extremal black holes or cold hyperbolic black holes. This is testimony of our still quite poor understanding of the duality [18][19][20]. In the benchmark model provided by the eternal black hole spacetime, the central object of interest for the VC ansatz is the extremal codimension-one surface S ∞ shown in Figure 1.…”

Section: A Quasilocal Ac Ansatz For Terminalsmentioning

confidence: 91%

Terminal holographic complexity

Barbón

Martín-García

2018

We introduce a quasilocal version of holographic complexity adapted to 'terminal states' such as spacelike singularities. We use a modification of the action-complexity ansatz, restricted to the past domain of dependence of the terminal set, and study a number of examples whose symmetry permits explicit evaluation, to conclude that this quantity enjoys monotonicity properties after the addition of appropriate counterterms. A notion of 'complexity density' can be defined for singularities by a coarse-graining procedure. This definition assigns finite complexity density to black hole singularities but vanishing complexity density to either generic FRW singularities or chaotic BKL singularities. We comment on the similarities and differences with Penrose's Weyl curvature criterion.1 It has been conjectured that (1) should saturate the Lloyd bound [15]. See, however [16,17].