Reparameterization Dependence is Useful for Holographic Complexity

Abstract

Holographic complexity in the "complexity equals action" approach is reconsidered relaxing the requirement of reparameterization invariance of the action with the prescription that the action vanish in any vacuum causal diamond. This implies that vacuum anti-de Sitter space plays the role of the reference state. Moreover, the complexity of an anti-de Sitter-Schwarzschild black hole becomes intrinsically finite and saturates Lloyd's bound after a critical time. It is also argued that several artifacts, such as the unphysical negative-time interval, can be removed by truly considering the bulk dual of the thermofield double state.

33 pages, 7 figures, v2: references added, v3: added section on BTZ black hole, version to appear in JHEP

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Cited by in corpus (6)

• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Mixed state information theoretic measures in boosted black brane
• Reparameterization Dependence and Holographic Complexity of Black Holes
• Holographic and QFT Complexity with angular momentum
• Cost of holographic path integrals