Bulk Action Growth for Holographic Complexity

TL;DR

This paper introduces a new method for calculating holographic complexity via the bulk action, addressing covariance issues and providing insights into the spatial structure of the Wheeler-de Witt patch.

Contribution

It presents a novel bulk action calculation method using tetrad formalism and teleparallel geometry, enhancing understanding of holographic complexity.

Findings

Bulk action calculation offers boundary term-free insights

Method addresses non-covariance issues in gravitational action

Framework can be covariantized within teleparallel geometry

Abstract

The action growth proposal relates the holographic complexity to the value of the action on the Wheeler-de Witt patch. We introduce a new method of calculating the gravitational action using the "bulk" term, i.e. the part of the Einstein-Hilbert action quadratic in connection coefficients. We demonstrate how to address the issue of non-covariance of the bulk action and evaluate it using the tetrad formalism. Due to the boundary term-free nature of the bulk action, we can gain further insights into the spatial structure of the action on the Wheeler-de Witt patch. We then argue that our entire scheme can be naturally covariantized within the framework of teleparallel geometry.