Conformal Mechanics and the Virasoro Algebra

TL;DR

This paper shows that one-dimensional scale-invariant mechanics inherently possess a Virasoro algebra symmetry, extending conformal symmetry, with implications for the AdS/CFT correspondence.

Contribution

It reveals that scale-invariant mechanics in one dimension naturally exhibit Virasoro algebra symmetry, a novel insight into their structure.

Findings

Any scale-invariant 1D mechanics has Virasoro symmetry.

Implications for the AdS/CFT correspondence are discussed.

Abstract

We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.