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

## TL;DR

This paper explores the analog of the $Tar{T}$ deformation in quantum mechanics, especially in holographic contexts like AdS$_2$ geometries and the Schwarzian theory, proposing a coupling to worldline gravity.

## Contribution

It introduces a novel $Tar{T}$-like deformation framework for quantum mechanics and relates it to worldline gravity, expanding holographic and quantum mechanical understanding.

## Key findings

- Proposes an equivalent description of the deformation via coupling to worldline gravity.
- Applies the deformation framework to the Schwarzian theory.
- Highlights the rich landscape of asymptotically AdS$_2$ geometries in holography.

## Abstract

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.