$T\bar{T}$ Deformation and the Complexity=Volume Conjecture

Abstract

Complexity in quantum physics measures how difficult a state can be reached from a reference state and more precisely it is the number of fundamental unitary gates we have to operate to transform the reference state to the state we are considering. In the holographic context, based on several explicit calculations and arguments, it is conjectured that certain bulk volume calculates the boundary field theory subregion complexity. In this paper, we will show that the $T\bar{T}$ deformation shows a strong signal of the correctness of this complexity equals volume conjecture. A bonus is a way to look at the $T\bar{T}$ deformation, by its reversibility, as operating a unitary quantum circuit which prepares states in quantum field theory.