Nonlocal dynamics and infinite non-relativistic conformal symmetries

TL;DR

This paper explores the symmetry structures of nonlocal models, revealing an infinite-dimensional algebra that extends non-relativistic conformal symmetries and resembles string theory, with implications for quantum Virasoro algebra.

Contribution

It introduces an infinite-dimensional symmetry algebra for nonlocal models, generalizing non-relativistic conformal symmetries and connecting to string theory and quantum Virasoro algebra.

Findings

Discovery of an infinite-dimensional symmetry algebra including Virasoro

Extension of non-relativistic conformal symmetries to infinite order

Quantum level analysis shows a centrally extended Virasoro algebra

Abstract

We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the non-relativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model and on the quantum level it leads to the centrally extended Virasoro algebra.