WdW-patches in AdS${}_3$ and complexity change under conformal transformations II

Abstract

We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincare-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of our previous paper arXiv:1806.08376, to the problem of how complexity of the CFT${}_2$ groundstate changes under a small local conformal transformation according to the action (CA) proposal. In stark contrast to the volume (CV) proposal, where this change is only proportional to the second order in the infinitesimal expansion parameter $\sigma$, we show that in the CA case we obtain terms of order $\sigma$ and even $\sigma \log (\sigma )$. This has strong implications for the possible field-theory duals of the CA proposal, ruling out an entire class of them.

31 pages + appendices, 9 figures v2: minor improvements, matches published version

References in corpus (15)

• Complexity and Shock Wave Geometries
• Quantum Computation as Geometry
• Causality & holographic entanglement entropy
• Gravitational action with null boundaries
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Einstein's Equations from Varying Complexity
• Switchbacks and the Bridge to Nowhere
• Holographic Holes in Higher Dimensions
• Holographic Holes and Differential Entropy
• Nuts and Bolts for Creating Space
• A geometric approach to quantum circuit lower bounds
• Boundary and Corner Terms in the Action for General Relativity
• The Boundary of the Future
• Comparison of holographic and field theoretic complexities by time dependent thermofield double states
• The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals

Cited by in corpus (5)

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• Complexity Growth of Dyonic Black holes with Quartic Field Strength Corrections
• Discrete scale invariance in holography and an argument against the complexity=action proposal
• Developments in non-relativistic field theory and complexity