Bulk action growth for holographic complexity

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 noncovariance 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.