Conformal quantum mechanics as the CFT$_1$ dual to AdS$_2$

TL;DR

This paper explores a 0+1-dimensional quantum mechanical model as a candidate for the conformal field theory dual to AdS$_2$, revealing how non-primary operators and non-invariant vacuum produce conformally invariant correlators.

Contribution

It demonstrates that despite the absence of a conformally invariant ground state, the theory's operators and vacuum structure yield conformally invariant correlation functions, proposing a novel duality framework.

Findings

Operators not primary can produce conformally invariant correlators.

The vacuum's non-invariance is compatible with conformal symmetry in correlators.

The model offers insights into AdS$_2$/CFT$_1$ duality mechanisms.

Abstract

A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory.