T-duality and T-folds for point particles

TL;DR

This paper demonstrates that T-duality, traditionally associated with string theory, also applies to point particle dynamics in certain four-dimensional backgrounds, revealing a new perspective on dualities beyond strings.

Contribution

It introduces the concept of point-particle T-duality and constructs explicit backgrounds where this duality manifests, extending the understanding of dualities to point particles.

Findings

Point-particle T-duality exists in specific four-dimensional backgrounds.

A family of backgrounds shows insensitivity of particle dynamics to parameter permutations.

T-duality for neutral particles is defined only on a dense subset of states.

Abstract

We argue that the T-duality phenomenon is not exclusively a stringy effect but it is relevant also in the context of the standard point particle dynamics. To illustrate the point, we construct a four-parametric family of four-dimensional electro-gravitational backgrounds such that the dynamics of a charged point particle in those backgrounds is insensitive to a particular permutation of the parameters although this very permutation does alter the background geometry. In particular, we find that a direct product of the Euclidean plane with the two-dimensional Euclidean black hole admits a point-particle T-dual with asymptotically negative curvature. For neutral particles, this point-particle T-duality picture gets slightly modified because the T-duality map is no longer defined everywhere but only on a dense open domain of the space of states. We suggest a possible interpretation of this phenomenon in terms of a point particle T-fold.