Complexity and Behind the Horizon Cut Off

TL;DR

This paper investigates holographic complexity in deformed AdS black brane solutions, revealing that a behind-the-horizon cutoff is necessary for consistent late-time growth, aligning with Lloyd's bound.

Contribution

It introduces a method to incorporate a behind-the-horizon cutoff in holographic complexity calculations motivated by $T{ar T}$ deformation, ensuring correct late-time behavior.

Findings

Late-time complexity grows linearly, consistent with Lloyd's bound.

Without the cutoff, complexity approaches a constant, contradicting expectations.

The cutoff behind the horizon is fixed by the boundary cutoff.

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.