Complexity and Behind the Horizon Cut Off

Abstract

Motivated by $T\overline{T}$ deformation of a conformal field theory we compute holographic complexity for a black brane solution with a cut off using "complexity=action" proposal. In order to have a late time behavior consistent with Lloyd's bound one is forced to have a cut off behind the horizon whose value is fixed by the boundary cut off. Using this result we compute holographic complexity for two dimensional AdS solutions where we get expected late times linear growth. It is in contrast with the naively computation which is done without assuming the cut off where the complexity approaches a constant at the late time.

14 pages, 2 figures, refs added, contribution of a counter term is added, minor correction, the final conclusion is not changed

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• Complexity for Charged Thermofield Double States
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
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• Note on Rényi entropy of 2D perturbed free fermions
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• Revisit on holographic complexity in two-dimensional gravity
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• Stringy Effects and the Role of the Singularity in Holographic Complexity
• Holographic Complexity for disentangled states
• Mixed state information theoretic measures in boosted black brane
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Holographic Complexity of Subregions in the Hyperscaling Violating Theories
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• Encoded information of mixed correlations: the views from one dimension higher
• Complexity as a holographic probe of strong cosmic censorship
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