Virasoro Algebra for Particles with Higher Derivative Interactions

TL;DR

This paper explores how higher derivative particle interactions exhibit Virasoro algebra symmetries and suggests a connection to conformal symmetry on a two-dimensional worldsheet, extending the understanding of reparametrization invariance.

Contribution

It demonstrates that higher derivative interactions lead to a Virasoro algebra structure in worldline reparametrizations and proposes a link to conformal symmetry in nonlocal theories.

Findings

Reparametrization symmetry forms a truncated Virasoro algebra.

Higher derivative interactions induce higher-dimensional symmetry structures.

Nonlocal particle theories can be described on a two-dimensional worldsheet.

Abstract

In this paper we show that the worldline reparametrization for particles with higher derivative interactions appears as a higher dimensional symmetry, which is generated by the truncated Virasoro algebra. We also argue that for generic nonlocal particle theories the fields on the worldline may be promoted to those living on a two dimensional worldsheet, and the reparametrization symmetry becomes locally the same as the conformal symmetry.