Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Complexity and Behind the Horizon Cut Off

Amin Akhavan, Mohsen Alishahiha, Ali Naseh, Hamed Zolfi

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.

Complexity and Behind the Horizon Cut Off

Abstract

Motivated by 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.

Paper Structure

This paper contains 4 sections, 53 equations, 2 figures.

Table of Contents

  1. Introduction
  2. CA complexity for cut off geometries
  3. Complexity for AdS$_2$ geometry
  4. Conclusions

Figures (2)

  • Figure 1: The intersection of WDW patch with the future interior of an eternal AdS black brane. The theory is defined at a radial finite cut off $r_c$ that fixes a cut off behind the horizon denoted by $r_0$.
  • Figure 2: Penrose diagram of AdS$_2$ geometry. The green part is covered by AdS global coordinates, while the Rindler coordinates cover a portion shown in the figure. The actual WDW patch is shown by blue color.