Quantum complexity of T T ¯ $$ T\overline{T} $$ -deformation and its implications

Abstract

Abstract We employ holography to calculate the quantum complexity of T T ¯ $$ T\overline{T} $$ -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.

Keywords

• AdS-CFT Correspondence
• Gauge-Gravity Correspondence
• Scale and Conformal Symmetries