$T\overline{T}$ in AdS$_2$ and Quantum Mechanics

Understand

Quantum field theory in zero spatial dimensions has a rich infrared landscape and a universal ultraviolet, inverting the usual Wilsonian paradigm.

• For holographic theories this implies a rich landscape of asymptotically AdS$_2$ geometries.
• Isolating the interiors of these spacetimes suggests a study of the analog of the $T\overline{T}$ deformation in quantum mechanics, which we pursue here.
• An equivalent description of this deformation in terms of coupling to worldline gravity is proposed, and applications to quantum mechanical systems - including the Schwarzian theory - are studied.