Quantum Complexity of $T\bar{T}$-deformation and Its Implications

TL;DR

This paper investigates the quantum complexity of $T\bar{T}$-deformed theories using holographic methods, revealing a geometric correction and proposing a new scheme for calculating holographic complexity.

Contribution

It introduces a novel geometric functional correction to complexity due to $T\bar{T}$-deformation and proposes an unambiguous holographic complexity calculation scheme.

Findings

Complexity differs from original theory by a bending (Willmore) energy term.

Provides a new scheme for holographic complexity calculation using CA proposal.

Links $T\bar{T}$-deformation effects to geometric properties of the bulk.

Abstract

We employ holography to calculate the quantum complexity of $T\bar{T}$-deformation, utilizing the complexity equals volume (CV) and the complexity equals action (CA) proposals within the bulk spacetime with a finite radius cutoff. We find that the complexity of the deformed theory differs from the renormalized complexity of the original theory by a geometric functional: the bending (Willmore) energy of the time-constant slice of the base manifold. We use this result to propose an unambiguous scheme for calculating holographic quantum complexity through the CA proposal.